MATH SOLVE

2 months ago

Q:
# 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

A:

let

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

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