Chapter 8.5, Problem 46PPS

To determine

The dimensions of the deck.

Answer to Problem 46PPS

  $16\text{ft by }32\text{ft}$

Explanation of Solution

Given:

New area = 512 feet square.

Calculation:

The solution for the given equation can be obtained as:

Let the number of feet added and subtracted will be:

  $\begin{array}{l}A=l\times w\\ 512=(24+x)(24-x)\\ 512=576-x^2\\ 0=64-x^2\\ 0=(8-x)(8+x)\\ 8-x=0,x=8\\ or\\ 8+x=0,x=-8\end{array}$

The amount added or subtracted cannot be negative.

  $\begin{array}{l}24–8=16\\ 24+8=32\end{array}$

  $\therefore \text{The dimensions of the deck are 16 feet by 32 feet}\text{.}$