Chapter 14.4, Problem 22PPS

a.

To determine

To find:the dimensions of the pool.

Answer to Problem 22PPS

  $2029ft,167ft$

Explanation of Solution

Given:

The perimeter ofrectangular reflecting Pool is $4392ft$ .

And the length is 25 feetmore than the 12 times width.

Calculation:

Let the width of therectangular reflecting Pool be $x$ .

According to the question, length is 30 meters longer than the width.

Therefore, length is $l=25+12x$ .

As the perimeter of Pool is $2\left(l+w\right)$ .

Therefore,

  $\begin{array}{l}2\left(l+w\right)=4932\\ \Rightarrow 2\left(25+12x+x\right)=4392\\ \left(25+13x\right)=2196\\ \therefore 13x=2196-25=2171\left\{\text{divide both side by 7}\right\}\\ x=\frac{2171}{13}=167\end{array}$

Thus, the length is $l=25+12x=25+12\left(167\right)=2029ft$

Hence, the dimensions are $2029ft,167ft$ .

b.

To determine

To find: the volume of the pool.

Answer to Problem 22PPS

  $v=677,686f{t}^3$

Explanation of Solution

Given:

The perimeter of rectangular reflecting Pool is $4392ft$ .

And the width is 83.5 times depth.

Calculation:

According to the question,width is 83.5 times depth.

Therefore,

  $\begin{array}{l}w=83.5\\ 167=83.5d\\ \therefore d=\frac{167}{83.5}=2ft\end{array}$

Therefore, the volume is $v=lwh=2029\times 2\times 167=677,686f{t}^3$

Hence, the volume of the pool $v=677,686f{t}^3$ .