Question

A rectangular swimming pool is 4 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 1800 cubic feet.

Find the dimensions of the pool.

Answer 1

19 x 23.5 x 4

Explanation:

4 * x * (x + 4.5) =1800

Divide both sides by 4

x * (x + 4.5) = 450

Use distributive property

x^2 + 4.5x = 450

Move all terms to one side

x^2 + 4.5x - 450 = 0

Use quadratic formula to solve a = 1, b = 4.5, c = -450

-4.5 +-
`√(4.5^2 - 4 * 1 * -450)`/2

=-4.5 + -
`√(1820.25)` / 2

= -4.5 +- 42.664 / 2

=19.08 and -23.582. You can't have a negative length, so it is 19.08, or 19

19 x 23.5 x 4