Chapter 8, Problem 10CCSR

To determine

ToFind :The area of the rectangle.

Answer to Problem 10CCSR

The area of the rectangle is $2x²+8x+8$ .

Therefore, the solution is H.

Explanation of Solution

Giveninformation:

Consider the width of the rectangle is $\left(x+2\right)$

And the height of the rectangle is twice of the width.

The area of the rectangle is width× height

Simplify,

According to formula,

  $\begin{array}{l}(x+2)\cdot 2(x+2)=(x+2)(2x+4)\\ \begin{array}{l}=x(2x+4)+2(2x+4)\hfill \\ =x(2x)+x(4)+2(2x)+2(4)\hfill \\ \begin{array}{l}=2x^2+4x+4x+8\\ =2x^2+8x+8\end{array}\hfill \end{array}\end{array}$

The area of the rectangle is $2x^2+8x+8$

Therefore, the solution is H.