Chapter 7.6, Problem 44E

To determine

To calculate: Width of the patio.

Answer to Problem 44E

The width of the patio is $8ft$ .

Explanation of Solution

Given information: Width of patio is same on every side.

Length of swimming pool $=24ft$

Width of swimming pool $=16ft$

Area of patio= Area of swimming pool

Calculation:

Area of rectangle $=l\times b$

Area of swimming pool $=24\times 16$

  $=384ft$

As, Area of patio= Area of swimming pool

Area of patio $=384ft$

Let the width of patio be $x$

Area of patio $+$ Area of swimming pool $=384+384$

  $=768ft$

Length of $patio+pool$

  $=(24+x)ft$

Width of $patio+pool$

  $=(16+x)ft$

  $\therefore$ $(24+x)(16+x)=768$

  $\Rightarrow 384+24x+16x+x^2=768$ (Simplifying left hand side using FOIL method)

  $\Rightarrow x^2+40x=384$

  $\Rightarrow x^2+40x-384=0$

Writing the left hand side factored and simplifying,

  $\begin{array}{l}\Rightarrow x(x+48)-8(x+48)=0\\ \Rightarrow (x-8)(x+48)=0\\ \Rightarrow x=8,-48\end{array}$

As length cannot be negative, $\therefore x$ is $8ft$

Thus, the width of the patio is $8ft$ .