Chapter 6.7, Problem 22STP

To determine

To calculate: The length of $\overline{FG}$ .

Answer to Problem 22STP

The length of $\overline{FG}$ is 4 m.

Explanation of Solution

Given information: Quadrilateral ABCD $\sim$ quadrilateral EFGH. In quadrilateral ABCD, the length of $\overline{BC}$ is 6 m, the length of $\overline{CD}$ is 12 m, the length of $\overline{DA}$ is 9 m. In quadrilateral EFGH, the length of $\overline{GH}$ is 8 m.

Calculation:

Let the length of $\overline{FG}$ be x m.

Quadrilateral ABCD $\sim$ quadrilateral EFGH.

As they are similar, the ratio of their corresponding sides are equal.

So we can write,

  $\frac{BC}{FG}=\frac{CD}{GH}$

  $\Rightarrow$$\frac{6}{x}=\frac{12}{8}$

  $\Rightarrow x\times 12=6\times 8$

  $\Rightarrow 12x=48$

  $\Rightarrow x=\frac{48}{12}$

  $\Rightarrow x=4$

So, the length of $\overline{FG}$ is 4 m.

Option C is correct.