Chapter 11.3, Problem 59SR

To determine

To find: Length of side ‘XT’.

Answer to Problem 59SR

The length of side XT = 7cm.

Explanation of Solution

Given Information:

  $\begin{array}{l}ST=SR\\ \angle SXT=90°\end{array}$

Figure:

  

Calculation:

Since this is an Isosceles Triangle, use the property of Triangles which states that angles opposite to equal sides are equal.

  $\begin{array}{l}\Rightarrow \angle \text{STX}=\angle \text{SRX}\mathrm{..................................................................}\left(1\right)\\ \&\\ \Rightarrow \angle \text{SXT}=\angle \text{SXR}=90°\mathrm{.........................................................}\left(2\right)\end{array}$

  $\begin{array}{l}\text{Now,}\\ \text{In ΔSTX \& ΔSRX}\\ \text{SX = SX}\left(\text{Common Side}\right)\\ \text{ST = SR}\left(\text{Given}\right)\\ \angle \text{SXT}=\angle \text{SXR}=90°\left(\text{From}\left(2\right)\right)\\ \Rightarrow \Delta \text{STX}\cong \Delta \text{SRX}\left(\text{By RHS Congruency}\right)\\ \Rightarrow \text{XT = XR}\left(\text{By c}\text{.p}\text{.c}\text{.t}\right)\\ \Rightarrow \text{X is the Mid Point}\end{array}$

Therefore,

XT = XR = 7cm.