Chapter 4.9, Problem 7P

To determine

To calculate: the area of the lawn.

Answer to Problem 7P

  $924{\text{ m}}^2$

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 entire park = $x$ m

Let length of the entire park = $\left(x+5\right)$ m

Now area of the entire park = $x\left(x+5\right)$ m²

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

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

width of the lawn = $\left(x-5\right)$ m

Now area of the lawn = $\left(x\right)\left(x-5\right)$ m²

area of the border = 330 m²

Entire park area − lawn area = border area

  $\begin{array}{l}x\left(x+5\right)-x\left(x-5\right)=330\\ x^2+5x-x^2+5x=330\\ 10x=330\\ x=\frac{330}{10}\\ x=33\text{ m}\end{array}$

So, length of the lawn is 33 m

width of the lawn

  $\begin{array}{l}\left(x-5\right)\\ 33-5\\ 28\text{ m}\end{array}$

Area of lawn = $33\times 28=924{\text{ m}}^2$