Area of Lawn

[Guest]

(s^2 + 20s + 20s + 400) - (64 + 8s + 8s + s^2)

you could have included the steps.......
remove brackets... s^2 + 20s + 20s + 400 - 64 - 8s - 8s - s^2
collect like terms.... s^2 - s^2 + 40s - 16s + 400 - 64
to give..... 24s + 336

but accept your answer..OK.....

40s + 400 - 64 - 16s....Yes,OK


24s + 336 ....Yes, this is the top expression simplified which as we have said many times before, it is the difference between the (overall area) and the (gravel + lawn area). So what are you left with when you calculate (overall area) - (gravel + lawn area)...????

The question does not say it is equal to 721.....?????

24s + 336 = 721 ......why did you put it equal to 721....??????


The rest below is wrong because of the errors above + other calc. errors.......

24s + 336 - 721

24s = -385

24s / 24 = -385 / 24

[Guest]

I can't solve it.

[Guest]

(s^2 + 20s + 20s + 400) - (64 + 8s + 8s + s^2)

40s + 400 - 64 - 16s

24s + 336 = 721.......can you explain why you do this line. In the last post I highlighted "The question does not say it is equal to 721.....?????"
So why do you do it....??. You need to read the question and try to understand the question before you can solve for the answer..??

24s + 336 - 721.......and can you explain why you do this line.

24s = -385

24s / 24 = -385 / 24

s = -385/24 = -16.04

[Guest]

I can't solve it. I apologize for wasting your time.

[Guest]

Read the question and the earlier postings again and see can you explain what is being calculated by this bit of the calculations

(s^2 + 20s + 20s + 400) - (64 + 8s + 8s + s^2)

40s + 400 - 64 - 16s

24s + 336

[Guest]

Area of garden minus area of walkway and lawn.

[Guest]

Area of garden minus area of walkway and lawn.

Yes, but not really, described as what we wanted. The question did not ask us to find that, but, If we describe it differently it may help......if we take the area of the whole garden and subtract the (gravel+lawn), what bit of the garden are we left with..???........ We are left with one of the parts that make up the 721.

So if you can get the other bit you should be able to make up an equation to help you solve for "s".

So see it you can find all the bits of the equation and put them together and solve for "s"

[Guest]

I don't know how to solve.

[Guest]

You are not yet at the stage where you can solve anything.............
That is why we need to find out a bit more first......

From the last post.....
if we take the area of the whole garden and subtract the (gravel+lawn), what bit of the garden are we left with..???.

There are only 3 bits that make up the whole garden. The question says there is (1) a flower border, (2) a gravel walkway, and (3) a lawn in the middle.

We already know the whole garden overall is (s + 20)^2 = (s^2 + 40s + 400)....and....The gravel+lawn is (s + ^2 =( s^2 + 16s + 64). There is only 1 bit we have not mentioned yet. We were trying to find its area by subtracting the gravel + the lawn from the whole garden......so we subtracted the two area expressions......(s^2 + 40s + 400) - ( s^2 + 16s + 64) and that gave us (24s + 336). So (24s + 336) is the area of the bit we have not mentioned yet and it is not hard to figure out that that bit is the "flower border". So we now know the areas of each of the whole garden, the gravel+lawn together, the lawn only on its own (we let it equal "s" to start with so has an area s^2, and now we know the flower border area on it own from the subtraction we did.

If we now read the question again we are told that the flower border plus the lawn added together has an area of 721 so all we have to do is add the required area expressions together and put it equal to 721 and solve for "s".

[Guest]

s^2 + 24s + 336 = 721

[Guest]

s^2 + 24s + 336 = 721
Yes, so that is the lawn area plus the flower area and it equals 721

(lawn) + (flower) = 721

(s^2 )+ (24s + 336) = (721)

we don't need the brackets I just put them in to illustrate.....

Now you have a quadratic, you can solve for "s"

There are 3 algebriac methods plus you can draw a graph

Try factorising first......

other methods..... try completing the square.....and use the formula

If that doesnt

[Guest]

x = - (1) + - sq. rt. 24^2 - 4(-1)(-385) / 2

x = -(1) + - sq. rt. 576 + 1540 / 2

x = -(1) + - sq. rt. 2116 / 2

x = -(1) + - sq. rt. 46 / 2

x = 22.5 x = - 23.5 or s

[Guest]

No your use of the formula is incorrect.

Did you to try to factorise first..??

[Guest]

I don't know how.

[Guest]

s^2 + 24s + 336 = 721
Yes, so that is the lawn area plus the flower area and it equals 721

So from here we have the equation to solve to find the value of "s"

If we re-arrange it all to LHS.....that is bring over the 721 to LHS or saying it another way, subtract 721 from each side, the equation will be equal to Zero.
and we will have it in the standard form od ax^2 +bx + c = 0 which we can solve as a quadratic equation

So.... s^2 + 24s + 336 - 721 = 0

Simplifying gives s^2 + 24s - 385 = 0

We want to find the value of "s" that makes this equation Zero......that is find the roots of the equation.

The most simple way is to try factorising the expression....If it factorises then we will have 2 factors that multiply together to give Zero...and will be easy to find.

You have to find the factors of 385 that when multiplied give 385 and when added or subtracted give 24. The factors of the "s^2" term is 1 so that is simple.

and you end up with ...... (s plus or minus one of the factors)(s plus or minus the other factor) and when you multiply out the brackets again you should get back to the quadratic as a check.

then solve for "s".....

[Guest]

s^2 + 24s -385 = 0

(s -11) (s + 35) = 0

s - 11 + 11 = 0 + 11 = 11 s + 35 - 35 = 0 - 35

s = 11 s = -35

[Guest]

s^2 + 24s -385 = 0 ....

(s -11) (s + 35) = 0 ........Yes.....2 factors

s - 11 + 11 = 0 + 11 = 11 s + 35 - 35 = 0 - 35 .........

s = 11 s = -35 ......yes these are the solutions or roots of the equation

(s -11) (s + 35) = 0 ..........2 factors

Normally what most people do is put each bracket = zero in turn

s-11 = 0 so s = 11
OR
s+35 = 0 so s = -35 ........this is not a realistic answer

So the real answer is s = 11 feet and area of lawn is 121 square feet.

[Guest]

Thanks again.

Also, please show where I was correct using the quadratic formula.

[Guest]

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You only attempted to use the quadratic formula here...and this in NOT correct
x = - (1) + - sq. rt. 24^2 - 4(-1)(-385) / 2

x = -(1) + - sq. rt. 576 + 1540 / 2

x = -(1) + - sq. rt. 2116 / 2

x = -(1) + - sq. rt. 46 / 2

x = 22.5 x = - 23.5 or s
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If a quadratic factorises...Then factorise it.....That is the best solution.

For the formula the equation has to be in the form ax^2 + bx + c = 0

Our equation is s^2 + 26s - 385 = 0 .....and it is now in the correct format

a = 1, b = 24, c = -385

The formula.....for 2 roots ....... [- b + or - sqrt(b^2 - 4ac)] / 2a

One root will be...... [- b + sqrt(b^2 - 4ac)] / 2a

The other root will be...... [- b - sqrt(b^2 - 4ac)] / 2a

Substitute in the values for a, b, and c and work out your answer.

but its harder than factorising

[Guest]

Thanks again.