Chapter 4, Problem 68SGR

To determine

To Find: The width of the deck.

Answer to Problem 68SGR

The width of the deck cannot be negative so the width of the deck is $5\text{ft}$ .

Explanation of Solution

Given:

The given total area of the garden with the deck cannot be more then $500\text{sq}\text{ft}$ .

The given diagram is shown in Figure 1

    Figure 1

Calculation:

From the given diagram the area of the garden is,

$15\text{ft}\left(20\text{ft}\right)=300{\text{ft}}^2$

Then, the total area of the deck is obtained as,

$\begin{array}{l}\left(15+x\right)\left(20+x\right)=500\\ 300+x^2+35x=500\\ \left(x+40\right)\left(x-5\right)=0\\ x=5\text{ft},-40\text{ft}\end{array}$

Since, the width of the deck cannot be negative so the width of the deck is $5\text{ft}$ .