An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond to the nearest tenth.

Accepted Solution

x-------> the length of the pond
y-------> the  width of the pond

we know that
[volume of the pond]=area of the base*deep
area of the base=volume/deep
volume=72000 in³
deep=24 in
area of the base=72000/24------> 3000 in²

area of the base=x*y
3000=x*y-------> equation 1
x=2y-----> equation 2

substitute equation 2 in equation 1
3000=[2y]*y------> 2y²=3000-----> y²=1500------> y=38.7 in
x=2y----> x=2*38.7----> x=77.4 in

the answer is
the length of the pond is 77.4 in
the  width of the pond is 38.7 in