The amount of water needed to fill the swimminl is 1152 cubic feet. Find the dimensions of the pool

Question

A rectangular swimming pool is 4 ft deep. One side of the pool is 4.5 times longer than the other.

Answer 1

L = 4.5W

V = 1152 = 4*W*(9/2)W = 18W²

^{Do the arithmetic to get W=8}

^{and L = 9*8/2 = 36.}

Answer 2

We know the volume of the pool is 1152 ft³.

We also know volume is found by length x width x height (or depth)

We also know the height (depth) of the pool is 4 feet.

We are given the fact that one side of the pool is 4.5 times longer than the other.

Let's just assign this side to the length and say that

L = 4.5 W

Let's take our formula and plug in what we know.

L x W x H = 1152 ft³.

substituting we get (4.5 W) ( W ) ( 4ft) = 1152 ft³

4.5 W² (4ft) = 1152 ft³.

Divide both sides by 4ft.

4.5 W² = 288 ft²

Divide both sides by 4.5

W² = 64 ft².

Take the square root of both sides.

W = 8

So, the length = 4.5 (8ft) = 36 ft.

Your dimensions are 36ft x 8ft x 4ft.

To check your answer, simply plug the values back into your formula and see if you get 1152 ft³.

36 x 8 x 4 does indeed = 1152.