Chapter 8.3, Problem 24PPS

To determine

To find: The expression that represents the total area of the garden and the walkway.

Answer to Problem 24PPS

  $4x^2+28x+48$

Explanation of Solution

Given:

The width of the garden is 8 feet, and the length is 6 feet. The width x of the walkway around the garden is same on every side.

Calculation:

Draw a figure for the given situation

  

The total length of garden and the walkway is $8+2x$

And the width of the garden and the walkway is $6+2x$

Therefore, the area of the garden and the walkway is given by

  $\begin{array}{l}\left(8+2x\right)\left(6+2x\right)\\ =48+16x+12x+4x^2\\ =4x^2+28x+48\end{array}$

So, the total area of the garden and the walkway is $4x^2+28x+48$