Chapter 14.7, Problem 7CYU

To determine

To calculate: An expression in factored form that represents the area of the walkway.

Answer to Problem 7CYU

  $4(3x+4)$ square meters

Explanation of Solution

Given information:

The diagram represents a walkway that is 2 meters wide surrounding a rectangular garden.

  

Calculation:

The area of the rectangular garden

  $\begin{array}{l}=(2x)(x)\\ =2x^2\end{array}$

Total area of the walkway including the garden

  $\begin{array}{l}=(2x+4)(x+4)\\ =2x^2+8x+4x+16\\ =2x^2+12x+16\end{array}$

Then, area of the walkway

  $\begin{array}{l}=\text{Total area }-\text{ Area of garden}\\ =(2x^2+12x+16)-2x^2\\ =12x+16\\ =4(3x)+4(4)[\text{GCF=4]}\\ \text{=}4(3x+4)[\text{Taking 4 common]}\end{array}$

Thus, the area of walkway is $4(3x+4)$ square meters.