Chapter 8.3, Problem 50PFA

To determine

To choose: The expression for the area of the photograph with the mat.

Answer to Problem 50PFA

The area of the photograph with matting is given $4x^2+36x+80$

D is the correct option.

Explanation of Solution

Given:

An 8 inch-by-10 inch photograph with matting is shown below.

  

  $\begin{array}{l}\mathrm{A }4x+8\\ \mathrm{B }4x^2+80\\ \mathrm{C }4x^2+28x+80\\ \mathrm{D }4x^2+36x+80\end{array}$

Calculation:

The length of the photograph with matting is given by $\left(8+2x\right)$

And the width of the photograph with matting is given by $\left(10+2x\right)$

So, the area of the photograph with matting is given by

  $\begin{array}{l}\left(8+2x\right)\left(10+2x\right)\\ =80+16x+20x+4x^2\\ =4x^2+36x+80\end{array}$

Hence, D is the correct option.