Chapter 4.6, Problem 18PPSE

Solution

To determine the dimensions of the pool.

The length of the pool is $30\text{ feet,}$ width is $12\text{ feet,}$ and depth is $6\text{ feet}\text{.}$

Given:

Depth of the rectangular swimming pool $=6\text{ feet}$

One side of the pool $2.5$ time longer than the other side

Volume of the swimming pool $=2160\text{ cubic feet}$

Formula Used:

  $\text{Volume of cuboid}=\text{length}\times \text{width}\times \text{depth}$

Calculation:

The swimming pool is cuboid in shape. The swimming pool is cuboid in shape. Now, let the width of the rectangular swimming pool be $x.$ So, the length of the rectangular swimming pool is:

  $\text{length}=2.5x$

Now, the volume of cuboid is $2160,$ i.e.

  $\begin{array}{l}\text{Volume of cuboid}=\text{length}\times \text{width}\times \text{depth}\\ \Rightarrow \text{2160}=\text{length}\times \text{width}\times \text{depth}\\ \Rightarrow 2160=x\times 2.5x\times 6\\ \Rightarrow 2160=15x^2\\ \Rightarrow x^2=\frac{2160}{15}\\ \Rightarrow x^2=144\\ \Rightarrow x=\pm 12\end{array}$

As the width cannot be negative, so the width of the swimming pool is:

  $\text{width}=12\text{ feet}$

And, the length of rectangular pool is:

  $\begin{array}{l}\text{length}=2.5x\\ \Rightarrow \text{length}=2.5\times 12\\ \Rightarrow \text{length}=30\text{ feet}\end{array}$

Hence, the length of the pool is $30\text{ feet,}$ width is $12\text{ feet,}$ and depth is $6\text{ feet}\text{.}$