# A rectangular swimming pool is 6 ft deep. One side of the pool is is 2.5 times longer than the other The amount of water needed to fill the swimming pool is 2160 cubic feet. How do you find the dimensions of the pool?

Oct 23, 2016

$\text{ Width " = 12 ft; " Length " = 30 ft; " Depth } = 6 f t$

#### Explanation:

Assuming an even depth for the entire pool the equation for cubic space or volume is:

$V = L \times W \times D$

where L = Length, W = Width and D = Depth.

In this problem the Depth, the Total Space (TS) or Volume and the relationship between the length and width are known.
Therefore the solution equation can be written as:

$2160 = 6 \times W \times 2.5 W$

Solving for $W$ gives the following solution steps:

$\frac{2160}{6} = W \times 2.5 W$

$360 = W \times 2.5 W$;

$360 = 2.5 {W}^{2}$

$\frac{360}{2.5} = {W}^{2}$

$144 = {W}^{2}$

$W = 12$

Therefore the solution is

$\text{ Width " = 12 ft; " Length " = 30 ft; " Depth } = 6 f t$