Chapter 8.4, Problem 17P

A square brown tarp has a square green patch green in the corner. The side length of the tarp is $(x+8)$ and the side length of the patch is $x$.

What is the area of the brown part of the tarp?

To determine

To find : area of brown part of the tarp

Answer to Problem 17P

  $16x+64$

Explanation of Solution

Given information: A square brown tarp has a square green patch in the corner. The side length of the tarp is (x+ 8) and side length of the patch is x.

Calculation:

The length of side of tarp is x+ 8 and length of side of patch is x.

Area of tarp is $\begin{array}{l}{A}_1={\left(side\right)}^2\\ A_1=\left(x+8\right)\left(x+8\right)\\ A_1=x\left(x+8\right)+8\left(x+8\right)\\ A_1=x^2+8x+8x+64\\ A_1=x^2+16x+64\end{array}$

Area of green patch is

  $\begin{array}{l}{A}_2={\left(side\right)}^2\\ A_2=x^2\end{array}$

Now, area of brown part of tarp is

  $\begin{array}{l}A=A_1-A_2\\ A=\left(x^2+16x+64\right)-x^2\\ A=16x+64\end{array}$

Thus, area of shaded region is $16x+64$ .