Chapter 4.9, Problem 3P

To determine

To calculate: the original dimension of pool.

Answer to Problem 3P

Length = 36 m & width = 12 m

Explanation of Solution

Given:

Length of the pool is 3 times the width

width of the deck 2.5 m

Area of the deck 265 m²

Calculation:

Let width of the pool be = $x$ m

Let length of the pool be = $3x$ m

Now area of the pool = $x\times 3x$ m²

width walkway of the deck for single side 2.5 m & both side is 5 m

So, length of the deck = $\left(3x+5\right)$ m

width of the new rectangle = $\left(x+5\right)$ m

Now overall area = $\left(3x+5\right)\left(x+5\right)$ m²

area of deck = 265 m²

Overall area − pool area = deck area

  $\begin{array}{l}\left(x+5\right)\left(3x+5\right)-x\times 3x=265\\ 3x^2+5x+15x+25-3x^2=265\\ 20x+25=265\\ 20x=265-25\\ 20x=240\\ x=\frac{240}{20}\\ x=12\text{ m}\end{array}$

So, width of the pool is 12 m

Length of the pool

  $\begin{array}{l}3x\\ 3\times 12=36\text{ m}\end{array}$

Area of pool $12\times 36=432{\text{ m}}^2$