Chapter 8, Problem 32RP

To determine

To find:The lengths of given segments i.e. GJ and HJ.

Answer to Problem 32RP

The length of GJ = 3.3 units, and Length of HJ = 6.6 units.

Explanation of Solution

Given information:

In this question all items below are given

  $\begin{array}{l}\overline{GB}\perp \overline{AC};\overline{HD}\perp \overline{EC};\overline{JF}\perp \overline{AE}\\ AB=8,BC=8,EC=15,AE=10,GH=5\end{array}$

Formula used:

Ratios of corresponding sides are equivalent.

Calculation:

Ratio of the corresponding sides are as:

  $\begin{array}{l}\frac{GJ}{GH}=\frac{AE}{EC}\Rightarrow GJ=5\times \frac{10}{15}=\frac{10}{3}=3.3\text{ units}\\ \frac{HJ}{AE}=\frac{GJ}{GH}\Rightarrow HJ=10\times \frac{3.3}{5}=6.6\text{ units}\end{array}$