Number of Acres

[Guest]

A tract of land is square and is to be enclosed by a three rail fence. Each rail is 12 feet in length. The number of acres enclosed is equal to the number of rails in the entire fence. Calculate number of acres.

Thanks.

[Guest]

Yes, always read the question.......

The land is enclosed by a three rail fence.
The number of acres enclosed is equal to the number of rails in the fence
So therefore the number of acres enclosed is three.

[Guest]

The answer given is a large number. Thanks.

[Guest]

A tract of land is square and is to be enclosed by a three rail fence. Each rail is 12 feet in length. The number of acres enclosed is equal to the number of rails in the entire fence. Calculate number of acres

Each rail is 12 feet in length..??.....So what we are saying is that the fence rails are made of "boards" (may not be a wooden fence) or sections of rail each 12 feet long, joined end to end around the perimeter of the area of land. The area is square so there are no rounded corners. Is the perimeter a multiple of 12 foot lengths and no cut lengths. If we have cut lengths is the piece cut off wasted or can it be used somewhere else.

The number of acres enclosed is equal to the number of rails..??......So what we are saying is the number of acres is equal to the number of "single rail sections" each 12 foot long, that make up the 3 rails around the perimeter or, is it the number of "three rail sections" each 12 foot long that make up the perimeter.

[Guest]

Lets give a simple solution......................

Lets say there are three bars on the fence around the field and each bar is made up of rails having a length of 12 feet.

Let R = Number of Rails per Bar per side of the field.

There are 4 sides to the square field and 3 bars on the fence

So there are 12R rails needed for the total fence.
This is the same figure as the number of acres.

Each rail is 12 foot long so length of side of field is 12R feet.

Let F = the number of square feet in one acre/

So.....( 12R x 12R ) / F = 12R

So 12R / F = 1

and so.....12R = F

So the number of acres is the same as the number of square feet in one acre.

So..............9 x 4840 = 43560 acres in the tract of land

.................Simple.................

[Guest]

Please give more detail in your simple solution. Thanks.

[Guest]

I don't know that I can be much more explicit..........

Post your solution and we will see how you get on......You may have a totally different outlook......

I think is is quite straight forward providing we both understand the question....What is it telling us and what is it asking.

The field is square or the tract of land is square.

So if R rails make up one bar of the fence along one side then....
There are 4 sides to the field and there are 3 bars on the fence
So that is 12R rails each 12 foot long to go all around the field.
That is the total number of rails and the question tells us that is the number of acres in the field.

If there are R rails on one bar of the fence, along one side of the field, and each is 12 foot long then the length of the field is 12R feet.

And if it is square its width must be the same and also its area must be ( 12R x 12R ) square feet.

To save working with and typing big numbers we can let F equal the conversion factor for the number of square feet in one acre.

If we let F equal the number of square feet in one acre then we can convert the area from square feet to acres by dividing by F.

So the acres will be ( 12R x 12R ) / F acres

And and we are told that this is equal to the number of rails in the whole fence which we found was 12R

So we have...... ( 12R x 12R ) / F = 12R.

Now divide across by 12R gives (12R / F) = 1

or 12R = F......by cross multiply or multiply across by F whichever way you want to do it

And it works out that from the above equation that 12R which is the total number of "12 foot" rails in the fence, which is the total acres in the field, is

equal to F which is the number of square feet in one acre.

I don't know how many square feet there are in an acre but......

I know there are 4840 square yards in an acre and there are 9 square feet in each square yard.....

.............So.....there are 9 x 4840 = 43560 square feet in an acre and this is the number of acres in the field or tract of land....


.....................So........Keep it Simple.....................

[Guest]

I didn't know how to solve it. I understand it now. Thanks again.

[Guest]

So in conclusion....................

The number of "12 foot Rails" needed for each bar of each side is R = (43560 / 12) = 3630

So all are full 12 foot length, no need to cut any, and no wastage.

So total number of "12 foot" rails needed for all of the fence is 3630 x 3 x 4 = 43560.

The length of each side is 12R feet = 43560 feet. If we divide this by 5280 we get the length in miles.

So.....43560 / 5280 = 8.25 miles

So......Area of land is 8.25 x 8.25 = 68.0625 square miles.


.....................Simple......................................