Chapter 9.3, Problem 16PSB

(a)

To determine

To find: The length of line segment $EH$ .

Answer to Problem 16PSB

The length of line segment $EH=11.25\text{ units}$

Explanation of Solution

Given information :

  $HG=4\text{ units and }EF=3 \text{units}$

Formula used :

Corresponding sides of similar triangles are equivalent

Calculation :

  $\begin{array}{l}\frac{EH}{EF}=\frac{EF}{HG}\\ EH=EF\times \frac{EF}{HG}\\ EH={\left(3\sqrt{5}\right)}^2\times \frac{1}{4}=\frac{45}{4}=11.25\text{ units}\end{array}$

(b)

To determine

To find: The length of line segment $EG$

Answer to Problem 16PSB

The length of line segment $EG\text{ is }4\text{ units}$

Explanation of Solution

Given information :

The segments are $GF=6\text{ units and }EH=3\text{ units}$

Formula used :

Corresponding sides of triangle are equivalent.

Calculation :

  $\begin{array}{l}\frac{EG}{GF}=\frac{GF}{EH}\\ \Rightarrow EG=GF\times \frac{GF}{EH}\\ \Rightarrow EG={\left(3\right)}^2\times \frac{1}{9}=4\text{ units}\end{array}$