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Width - Driveway
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Re: Width - Driveway
by Guest » Sat Mar 28, 2015 6:14 pm
Yes 50 sq ft is blue. Blue and black covered the same area.
So back to driveway......What is area of the driveway.......
So back to driveway......What is area of the driveway.......
- Guest
Re: Width - Driveway
by Guest » Sat Mar 28, 2015 6:57 pm
and the house is the same area........
so all you need to do is write an equation for either the area of the house or the area of the driveway in terms of the width of the driveway and put it equal to 5000 and solve it...........
so all you need to do is write an equation for either the area of the house or the area of the driveway in terms of the width of the driveway and put it equal to 5000 and solve it...........
- Guest
Re: Width - Driveway
by Guest » Sat Mar 28, 2015 7:25 pm
Area = S^2
5000 = 70.71^2
I don't think that is correct.
5000 = 70.71^2
I don't think that is correct.
- Guest
Re: Width - Driveway
by Guest » Sat Mar 28, 2015 7:59 pm
so all you need to do is write an equation for either the area of the house or the area of the driveway in terms of the width of the driveway and put it equal to 5000 and solve it...........
The question asks to find the width of the driveway.......
The driveway and the house have the same area.......half of the area of the plot of land.
So we can pick either to write an equation for its area. Equation needs to be in terms of the width of the driveway
For example......Suppose I have a piece of wood 5 feet long and I cut "X" feet off it. The bit that is left is ( 5 - X) feet.
So you need to do same with driveway and the plot sides OR the gouse and the plot sides to write an equation for the area.
The question asks to find the width of the driveway.......
The driveway and the house have the same area.......half of the area of the plot of land.
So we can pick either to write an equation for its area. Equation needs to be in terms of the width of the driveway
For example......Suppose I have a piece of wood 5 feet long and I cut "X" feet off it. The bit that is left is ( 5 - X) feet.
So you need to do same with driveway and the plot sides OR the gouse and the plot sides to write an equation for the area.
- Guest
- Guest
Re: Width - Driveway
by Guest » Sun Mar 29, 2015 6:55 am
What do you mean by stating answers like that....??
How can you say sides are 300 feet if the sides of the whole plot are only 100 feet.
The question states that the house is inside the plot facing the street and the driveway is around the other 3 side. So that means the front of house is against the edge of the plot at the road and the driveway is up both sides of the house and along the back of the house. We are only asked to find the width of the driveway....just one width dimension so that implies the the driveway is the same width all around the house. So we can let the width of the driveway be "W" feet so that we can easily put it into equations. So what you need to do now is consider that the plot of land is made up of two areas and we know the area of both of them. The area of the driveway is 5000 sq feet and the area of the house is 5000 sq feet. The house is just one simple rectangle..it is not square because we know the driveway is the same width all around 3 of the sides, so that means its width is narrower than its front to back dimension. So the equation for the area of the house should be easy to find....just simply write the expression for the length of the sides of the house in terms of the plot sides length and the driveway width and multiply both together and that is equal to 5000 sq feet as we have already found. So solve for the value of "W".
The other way you couldconsider solving the problem is write an expression for the area of the driveway in terms of "W" and the length of the sides of the plot. The driveway is not a simple rectangle....It is made up of 3 rectangles...one up each left and right side of the house and one at the back of the house. So you would need to get expressions for area of each of these and add them together to equal 5000 sq feet for the driveway only. Then solve for the value of "W".
You don't need to do both equations.....just the one you prefer or think is easier.
The type of expressions will be similar to my example last post. The expressions will include algebra in terms of "W" and 100 which is the length of the sides of the plot. So you don't simply come up with and number right away, like the 300 as you did
in your last post. You have to first get an algebriac expression and then solve it
In the very simple example I gave before...We write the equation in terms of "X"........
Suppose the bit we were left with was equal to 3 feet.....Find "X the bit we cut off.
For example......Suppose I have a piece of wood 5 feet long and I cut "X" feet off it. The bit that is left is ( 5 - X) feet.
Then 5 - X = 3
So...X = 5 -3
So X = 2
So the bit we cut off is equal to 2 feet.
How can you say sides are 300 feet if the sides of the whole plot are only 100 feet.
The question states that the house is inside the plot facing the street and the driveway is around the other 3 side. So that means the front of house is against the edge of the plot at the road and the driveway is up both sides of the house and along the back of the house. We are only asked to find the width of the driveway....just one width dimension so that implies the the driveway is the same width all around the house. So we can let the width of the driveway be "W" feet so that we can easily put it into equations. So what you need to do now is consider that the plot of land is made up of two areas and we know the area of both of them. The area of the driveway is 5000 sq feet and the area of the house is 5000 sq feet. The house is just one simple rectangle..it is not square because we know the driveway is the same width all around 3 of the sides, so that means its width is narrower than its front to back dimension. So the equation for the area of the house should be easy to find....just simply write the expression for the length of the sides of the house in terms of the plot sides length and the driveway width and multiply both together and that is equal to 5000 sq feet as we have already found. So solve for the value of "W".
The other way you couldconsider solving the problem is write an expression for the area of the driveway in terms of "W" and the length of the sides of the plot. The driveway is not a simple rectangle....It is made up of 3 rectangles...one up each left and right side of the house and one at the back of the house. So you would need to get expressions for area of each of these and add them together to equal 5000 sq feet for the driveway only. Then solve for the value of "W".
You don't need to do both equations.....just the one you prefer or think is easier.
The type of expressions will be similar to my example last post. The expressions will include algebra in terms of "W" and 100 which is the length of the sides of the plot. So you don't simply come up with and number right away, like the 300 as you did
in your last post. You have to first get an algebriac expression and then solve it
In the very simple example I gave before...We write the equation in terms of "X"........
Suppose the bit we were left with was equal to 3 feet.....Find "X the bit we cut off.
For example......Suppose I have a piece of wood 5 feet long and I cut "X" feet off it. The bit that is left is ( 5 - X) feet.
Then 5 - X = 3
So...X = 5 -3
So X = 2
So the bit we cut off is equal to 2 feet.
- Guest
Re: Width - Driveway
by Guest » Sun Mar 29, 2015 2:16 pm
If you have no idea you would be better reading and trying out some simple basic algebra questions.
The example I gave about a piece of wood and cutting a piece from the end is probably about as simple as you can get that is a word type question that requires some reasoning. If you have problems solving that you would be better trying some examples on simplifying simple algebriac expressions and solving some simple equations that are already setup. Also just simple adding and subtract simple sums as numbers only, you would need to be able to do that as well first. The difference with algebra is there are unknowns that we let equal to a letter to get it defined and then we manipulate it as an equation equal to something and so find a value for the unknown
The driveway question is more complicated that the one about the piece of wood so you would need to be able to understand the simple ones first.
The example I gave about a piece of wood and cutting a piece from the end is probably about as simple as you can get that is a word type question that requires some reasoning. If you have problems solving that you would be better trying some examples on simplifying simple algebriac expressions and solving some simple equations that are already setup. Also just simple adding and subtract simple sums as numbers only, you would need to be able to do that as well first. The difference with algebra is there are unknowns that we let equal to a letter to get it defined and then we manipulate it as an equation equal to something and so find a value for the unknown
The driveway question is more complicated that the one about the piece of wood so you would need to be able to understand the simple ones first.
- Guest
Re: Width - Driveway
by Guest » Sun Mar 29, 2015 8:37 pm
I located a partial solution:
x = driveway width.
On each side of the lot the driveway extends from front to back 100 feet, total 200x sq. ft.
The house is 100 ft. - 2x ft.
The driveway behind house is 100 ft. - 2 x ft. in length * x ft. in width.
Total sq. ft. - 100x - 2x^2.
Total sq. ft. in driveway (at sides of lot and back of house) - 200x + 100x - 2x^2.
I don't understand.
x = driveway width.
On each side of the lot the driveway extends from front to back 100 feet, total 200x sq. ft.
The house is 100 ft. - 2x ft.
The driveway behind house is 100 ft. - 2 x ft. in length * x ft. in width.
Total sq. ft. - 100x - 2x^2.
Total sq. ft. in driveway (at sides of lot and back of house) - 200x + 100x - 2x^2.
I don't understand.
- Guest
Re: Width - Driveway
by Guest » Mon Mar 30, 2015 7:11 am
I think this shows a total lack of understanding of the problem. It looks like what you posted is an attempt to solve some other problem. You would need to first of all draw a sketch to represent the problem originally posted and you would see that the solution you gave is not possible. Even you cannot solve it by algebra you could try "guesses" at the dimensions of the driveway and come up with a reasonably accurate solution. That way you would at least demonstrate that you understand what the problem looks like.
I assume you still do not understand my simple example about cutting the piece of wood.
I assume you still do not understand my simple example about cutting the piece of wood.
- Guest
Re: Width - Driveway
by Guest » Mon Mar 30, 2015 10:42 am
The problem is "not an attempt to solve some other problem" as you stated. It is for this one.
Area of rectangle - length x width
5000 x 1 = 5000
2500 x 2 = 5000
500 x 10 = 5000
50 x 100 = 5000
Perimeter of rectangle - 2l + 2w - The driveway is around 3 sides.
What do I do ?
I understand about the piece of wood.
Don't bother.
Area of rectangle - length x width
5000 x 1 = 5000
2500 x 2 = 5000
500 x 10 = 5000
50 x 100 = 5000
Perimeter of rectangle - 2l + 2w - The driveway is around 3 sides.
What do I do ?
I understand about the piece of wood.
Don't bother.
- Guest
Re: Width - Driveway
by Guest » Mon Mar 30, 2015 12:33 pm
Your Quote....."The problem is "not an attempt to solve some other problem" as you stated. It is for this one."
..... Then except you can explain, I do not understand that it is part of the solution for this one..............
Area of rectangle - length x width....This just states the fact that the area of a rectangle is length x width
5000 x 1 = 5000......?
2500 x 2 = 5000......?
500 x 10 = 5000......?
50 x 100 = 5000......?
Why did you do the above 4 calculations....What are you trying to work out...?
Perimeter of rectangle - 2l + 2w - The driveway is around 3 sides......What are you trying to do here??
Your Quote..."I understand about the piece of wood".......Well then if you do understand the piece of wood example, relate it to the length of the sides of the plot and the house.
From earlier posts we said there were 2 simple ways to solve the problem either using the area of the driveway or using the area of the house.
As example we will first try using the area of the house......
First we will try to write an expression for the width of the house.....
Imagine you are standing on the road at the front of the house, looking at the house. What should you see?....You should see the front of the house with a driveway at each side. If we let the width of each driveway (they are both the same width) be equal to "W" feet, What is the the width of the house.
This is the same type of calculation as was for the piece of wood. If you understand how the calculations for the piece of wood were done then you should be able to do this one for the width of the house.
A similar calculation is needed for the length of the house front to back.....but it will not be exactly the same calculation because the house is not square........So what is it?......
..... Then except you can explain, I do not understand that it is part of the solution for this one..............
Area of rectangle - length x width....This just states the fact that the area of a rectangle is length x width
5000 x 1 = 5000......?
2500 x 2 = 5000......?
500 x 10 = 5000......?
50 x 100 = 5000......?
Why did you do the above 4 calculations....What are you trying to work out...?
Perimeter of rectangle - 2l + 2w - The driveway is around 3 sides......What are you trying to do here??
Your Quote..."I understand about the piece of wood".......Well then if you do understand the piece of wood example, relate it to the length of the sides of the plot and the house.
From earlier posts we said there were 2 simple ways to solve the problem either using the area of the driveway or using the area of the house.
As example we will first try using the area of the house......
First we will try to write an expression for the width of the house.....
Imagine you are standing on the road at the front of the house, looking at the house. What should you see?....You should see the front of the house with a driveway at each side. If we let the width of each driveway (they are both the same width) be equal to "W" feet, What is the the width of the house.
This is the same type of calculation as was for the piece of wood. If you understand how the calculations for the piece of wood were done then you should be able to do this one for the width of the house.
A similar calculation is needed for the length of the house front to back.....but it will not be exactly the same calculation because the house is not square........So what is it?......
- Guest
Re: Width - Driveway
by Guest » Mon Mar 30, 2015 1:31 pm
My calculations were "guesses" at the dimensions as you suggested.
I thought the perimeter may be needed.
I thought I understood about the piece of wood - I guess not.
I thought the perimeter may be needed.
I thought I understood about the piece of wood - I guess not.
- Guest
Re: Width - Driveway
by Guest » Mon Mar 30, 2015 2:04 pm
It is very unlikely that you will be able to solve the problem by "guesses"......Random non logical guesses will not achieve anything. But ther is a process of "Trial and Improvement" you could follow and you should be able to get to a reasonably accurate solution. That means making a reasonable guess for the width "W", then working out the areas and see if they come to the values expected and if they don't then try a second guess and work out the areas again and see if that was a better guess than the first. If it was better than the first then try a third guess in that direction and calculate again and if it was a worse guess then try another guess in the other direction and eventually you should come to the solution.
But the method we were trying to do here in earlier posts is to use algebra and work out a value for "W" directly from the equations.
What is it you do not understand about the piece of wood problem. All that was done was a piece was cut off and you had to find how much was cut off.? You need to be able to do this type of problem first. The problem cannot be made any more simple.
But the method we were trying to do here in earlier posts is to use algebra and work out a value for "W" directly from the equations.
What is it you do not understand about the piece of wood problem. All that was done was a piece was cut off and you had to find how much was cut off.? You need to be able to do this type of problem first. The problem cannot be made any more simple.
- Guest
Re: Width - Driveway
by Guest » Mon Mar 30, 2015 2:41 pm
I don't understand how to apply the wood problem to the driveway problem.
- Guest
Re: Width - Driveway
by Guest » Mon Mar 30, 2015 3:09 pm
We had a piece of wood 5 foot long when we cut a bit "X" off it we were left with 3 feet.......How much did we cut off.?
When we are standing on the road looking at the front of the house and we know the length of the side of the plot and there is a driveway "W" on each side and the front width of the house in between......What is the width of the house?
When we are standing on the road looking at the front of the house and we know the length of the side of the plot and there is a driveway "W" on each side and the front width of the house in between......What is the width of the house?
- Guest
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