Chapter 7.4, Problem 43PPS

To determine

To find: The lengths of FG , EH , and DJ of the given figure.

Answer to Problem 43PPS

The lengths of FG , EH , and DJ of the given figure are $8.75\text{ft}$ , $17.5\text{ft}$ , and $26.25\text{ft}$ .

Explanation of Solution

Given information:

The given figure is,

  

From the triangular proportionality theorem, the length of FG is calculated as,

  $\begin{array}{l}\frac{FG}{AC}=\frac{1}{4}\\ \frac{FG}{35}=\frac{1}{4}\\ FG=8.75\text{ft}\end{array}$

From the triangular proportionality theorem, the length of EH is calculated as,

  $\begin{array}{l}\frac{EH}{AC}=\frac{1}{2}\\ \frac{EH}{35}=\frac{1}{2}\\ EH=17.5\text{ft}\end{array}$

From the triangular proportionality theorem, the length of DJ is calculated as,

  $\begin{array}{l}\frac{DJ}{AC}=\frac{3}{4}\\ \frac{DJ}{35}=\frac{3}{4}\\ DJ=26.25\text{ft}\end{array}$

Thus, the lengths of FG , EH , and DJ of the given figure are $8.75\text{ft}$ , $17.5\text{ft}$ , and $26.25\text{ft}$ .