Chapter 8, Problem 16RP

To determine

To calculate: The length of EO and EK segment.

Answer to Problem 16RP

The length of segments: EO = 1.2 units and EK = 9 units

Explanation of Solution

Given information:

The segments, $\overleftrightarrow{EF}\parallel \overleftrightarrow{GO}\parallel \overleftrightarrow{HM}\parallel \overleftrightarrow{JK}$

The length of segments: FG = 2, GH = 8, HJ = 5, EM = 6

Formula used:

Ratio of lengths of corresponding segments are equivalent

Calculation:

  $\begin{array}{l}\frac{EO}{EM}=\frac{FG}{FH}=\frac{FG}{FG+GH}\\ \Rightarrow EO=EM\times \frac{FG}{FG+GH}\\ \Rightarrow EO=6\times \frac{2}{2+8}=6\times \frac{2}{10}\\ \Rightarrow EO=1.2\text{ units}\end{array}$

Again, we have

  $\begin{array}{l}\frac{EK}{EO}=\frac{FJ}{FG}=\frac{FG+GH+HJ}{FG}\\ \Rightarrow EK=EO\times \frac{FG+GH+HJ}{FG}\\ \Rightarrow EK=1.2\times \frac{2+8+5}{2}=1.2\times \frac{15}{2}\\ \Rightarrow EK=1.2\times 7.5=9\text{ units}\end{array}$