Chapter 8.3, Problem 7CYU

To determine

To find: The expression that represents the total area of the picture and the frame.

Answer to Problem 7CYU

  $4x^2+72x+320$

Explanation of Solution

Given:

The frame has a width of x inches all the way around.

  

Calculation:

Draw the picture as shown below

  

Total length is $\left(20+2x\right)$ and the total width is $\left(16+2x\right)$

Therefore, the total area of the picture and the frame is given by

  $\begin{array}{l}\left(20+2x\right)\left(16+2x\right)\\ =320+40x+32x+4x^2\\ =4x^2+72x+320\end{array}$

So, the expression which represents the required area is $4x^2+72x+320$