Chapter 1.7, Problem 59P

Geometry Write an expression in simplified form for the area of each rectangle.

To determine

To write: in the simplified form of the expression representing the area of the rectangle with length $15$ and width $x-5$ .

Answer to Problem 59P

  $15x-75$

Explanation of Solution

Given:

Length of rectangle = $15$ and width of rectangle = $x-5$ .

Distributive property:

  $a\left(b-c\right)=ab-ac$

The area of the rectangle is:

  $\begin{array}{c}\text{Area}=\text{Length}\times \text{Width}\\ \text{=15}\left(x-5\right)\end{array}$

Apply the distributive property,

  $\begin{array}{c}\text{Area}=\text{15}\left(x-5\right)\\ \text{=15}\left(x\right)-\text{15}\left(5\right)\\ =15x-75\end{array}$