Chapter 8.4, Problem 66PFA

To determine

To find: The perimeter of the tabletop.

Answer to Problem 66PFA

The perimeter of the tabletop is given by $32x-12$

  $C$ is the correct option.

Explanation of Solution

Given:

The top of a square coffee table has an area of $64x^2-48x+9$

Options are

  $\begin{array}{l}\mathrm{A }8x-3\\ \mathrm{B }16x-9\\ \mathrm{C }32x-12\\ \mathrm{D }20x\end{array}$

Calculation:

Let the sides of the square top table is $a$

Area of a square is given by $a^2$

Therefore,

  $\begin{array}{l}{a}^2=64x^2-48x+9\\ a^2={\left(8x\right)}^2-2\cdot 8x\cdot 3+3^2\\ a^2={\left(8x-3\right)}^2\\ a=8x-3\end{array}$

Hence, the perimeter of the square top is given by

  $\begin{array}{l}4a\\ =4\left(8x-3\right)\\ =32x-12\end{array}$

Hence, $C$ is the correct option.