Question

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.

Answer 1

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

Answer 2

The length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.

What is the rectangular prism?

In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles. A rectangular prism is also a cuboid.

Let,a be the length of the pond and b be the width of the pond.

The volume of the pond is;

$\rm Volume \ of \ the \ pond= Area\ of\ the\ base\times deep\\\\Area\ of\ the\ base=\dfrac{Volume \ of \ the \ pond}{base}\\\\Area\ of\ the\ base=\dfrac{72000}{24}\\\\Area\ of\ the\ base=3000 in^2$

The length of the pond is two times its width.

a = 2b

The area of the base = a × b

3000 = ab

ab = 3000

Substitute the value of a in equation 2

$\rm ab=3000\\\\2b \times b = 3000\\\\b^2=\dfrac{3000}{2}\\\\b^2=1500\\\\b=38.7$

Substitute the value of b in equation 1

$\rm a=2b\\\\a=2 \times 38.7\\\\a=77.4$

Hence, the length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.

To know more about rectangular prism click the link given below.

https://brainly.com/question/22534870

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