Question 1053737: A square farm contains as many acres as there are boards in the fence enclosure. The fence is 7 boards high, and each board is 8.25 ft. in length. Determine acres in the farm.
My partial attempt:
x = number of boards = number of acres.
x/4 = number of boards on one side.
43560 = square ft. in acre.
Unsure how to continue. Thanks.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Let the side of the farm=x ft.
The area is x^2 sq. ft.
The number of boards along a side is (x/8.25)*7=(7x/8.25)
The total number of boards is then (28x/8.25).
That equals the number of acres.
The number of acres of the farm is x^2/43560.
Therefore, (x^2/43560)=(28x/8.25)
cross-multiply
8.25x^2=1219680x
8.25x^2-1219680x=0
x(8.25x-1219680)=0
x=147840 feet
x^2/43560 is 501760 acres or 784 sq miles (28 miles on a side)
-----------------------------------
Each side has 28 miles*5280 feet/mile, or 147840 feet
divide that by 8.25 feet/board, and need 17920 boards just to line it.
But there are 4 sides, so 71680 boards.
And there are 7 boards stacked, so that is 71680*7=501760 boards. Checks
|
|
|
