Chapter 9.7, Problem 9PSA

a

To determine

To calculate: The length of the segment TR.

Answer to Problem 9PSA

The unknown segment will be $5\sqrt{2}$

Explanation of Solution

Given information :

TRWX is a kite

  $\begin{array}{l}\overline{TR}\cong \overline{WR},\overline{TX}\cong \overline{XW}\\ RY=5,TW=10,YX=12\end{array}$

Formula used :

In $45°-45°-90°$ triangle, two sides are equal

Calculation :

In triangle TYR, we have

RY = YT as it is $45°-45°-90°$ triangle

Therefore,

  $\begin{array}{l}T{R}^2=5^2+5^2=50\\ \Rightarrow TR=5\sqrt{2}\end{array}$

b

To determine

To calculate: The length of the segment WX.

Answer to Problem 9PSA

The unknown segment will be 24

Explanation of Solution

Given information :

TRWX is a kite

  $\begin{array}{l}\overline{TR}\cong \overline{WR},\overline{TX}\cong \overline{XW}\\ RY=5,TW=10,YX=12\end{array}$

Formula used :

In $30°-60°-90°$ triangle, sides are in ratio $x:x\sqrt{3}:2x$

Calculation :

In triangle TYR, we have

YX = x = 12

  $\begin{array}{l}WX=2x\\ WX=2(12)\\ WX=24\end{array}$