Area

[Guest]

If 900 rails are required for a fence to enclose an acre, a square field contains as many acres as rails in the fence enclosing the field. Calculate area of the field. I know this problem is similar to the fence - acre problem posted previously.

An acre contains 43,560 square feet.

A square has 4 equal sides.

Area = length x width.

Let a = area of field.

How do I proceed ?

[Guest]

your question needs to supply more info.
Is 900 rails on a square acre fence
OR a long rectangular acre fence
length of sides of a square acre is 4 x root 43560 = 835 feet

length of sides of a 10 feet x 4356 feet rectangle = 2 x 4366 = 8732 feet

what length is rails

how many rails in fence

[Guest]

"Is 900 rails on a square acre fence
OR a long rectangular acre fence" - The problem just states an acre.



"what length is rails - No length stated

how many rails in fence" - Just 900 for the acre.

[Guest]

Ok, then we will assume the acre fenced by 900 rails is square.....and use a wee bit of reasoning.

that means 900/4 = 225 rails on each side of the square.
Let the area of the large field = A^2 "read as A squared"
So the length of the side of the large field is A.
and also means the large field is A^2 "read as A squared times" bigger than an acre.
So the rails on the fence around the large field is 4 x 225 x A = 900A
and we are told this equals the area A^2.

So.... 900A = A^2
So .....divide across by A....gives....A = 900

So acres of large field is A^2 = 900 x 900 = 810000 acres.
and the number of rails is 900A = 900 x 900 = 810000.

[Guest]

''and also means the large field is A^2 "read as A squared times" bigger than an acre.
So the rails on the fence around the large field is 4 x 225 x A = 900A"

I am not clear on this step.

[Guest]

If the area of the small field is 1 acre and the area of the large field is A^2, then the large field must be A^2 larger than the small field.
Also the sides or the perimeters.... for the small field sides are root 1 units or just 1, and for the large field sides are root A^2 or A units.
So perimeters are 4 x root 1 = 4 units for small and 4 x A = 4A for large.

eg. if a small field is 1 acre and a large field is 9 acres, then the large field is 9 times bigger.
and the sides of large are root 9 = 3 so perimeter large is 12 units

the ratio of the sides to the area is always...... A to (A^2) or A : (A^2)

and each unit length of sides dimension uses 225 rails.........

[Guest]

I understand it now. Thanks.

[Guest]

It's a basic question of reasoning.
If you want to learn these then buy one good reasoning books and study hard. Or you can follow some good online websites. http://reasoningtricks.com/ is a good website for such things.

[Guest]

Thanks for the website.