Chapter 8.2, Problem 27PPE

To determine

To find:The area of the metal frame in factored form.

Answer to Problem 27PPE

  $25x^2(9-\pi )$

Explanation of Solution

Given information:A circular mirror is surrounded by a square metal frame. The radius of the mirror is $5x$ .The side length of the metal frame is $15x$ .

Calculation:

  

The area of the circular mirror is,

  $\begin{array}{l}\pi r^2\\ $ =\pi {(5x)}^2$=25\pi x^2\end{array}$

The total area of the square metal frame including the mirror is,

  $\begin{array}{l}{a}^2\\ $ ={(15x)}^2$=225x^2\end{array}$

Then, area of the square metal frame is,

  $\begin{array}{l}225x^2-25\pi x^2\\ =25x^2(9-\pi )[\text{factoring out the GCF]}\end{array}$

Thus, the area of the metal frame is $25x^2(9-\pi )$ .