Chapter 1.2, Problem 14PSB

To determine

To find: The values of $r$ and $m$ .

Answer to Problem 14PSB

  $m=\frac{5}{3}\text{ and }r=2$ .

Explanation of Solution

Given information:

A figure is given as below. $\overline{XS}\cong \overline{YT}\text{ and }\overline{YS}\cong \overline{XT}.$

  

Calculation:

A figure is given as below.

  

In above figure, $\overline{XS}\cong \overline{YT}\text{ and }\overline{YS}\cong \overline{XT}.$

  $\begin{array}{l}\overline{XS}\cong \overline{YT}\\ \Rightarrow 3m+7=4.2m+5\\ \Rightarrow 1.2m=2\\ \Rightarrow m=\frac{5}{3}\\ \text{Also, }\overline{YS}\cong \overline{XT}\\ \Rightarrow 3\frac{1}{2}r+2=2r+5\\ \Rightarrow 7r+4=4r+10\\ \Rightarrow 3r=6\\ \Rightarrow r=2\end{array}$

Hence, $m=\frac{5}{3}\text{ and }r=2$ .