Chapter 8.7, Problem 33PPS

To determine

To find: The expressions for the dimensions of the deck whose area is represented by given expression.

Answer to Problem 33PPS

The dimensions of the deck are $\left(24-x\right)$ feet and $\left(24+x\right)$ feet.

Explanation of Solution

Given information:

The area of the deck in square feet is represented by the expression $576-x^2$ .

Concept used:

The factors of the expression representing the area of the deck are the dimensions of the deck.

Calculations:

The area of the deck in square feet is represented by the expression $576-x^2$ that can be written as ${\left(24\right)}^2-x^2$

  $\Rightarrow {\left(24\right)}^2-x^2=\left(24-x\right)\left(24+x\right)$

Thus, the dimensions of the deck are $\left(24-x\right)$ feet and $\left(24+x\right)$ feet.

Conclusion:

The dimensions of the deck are $\left(24-x\right)$ feet and $\left(24+x\right)$ feet.