Chapter 11.3, Problem 60SR

To determine

To find: ‘Length of side AC’

Answer to Problem 60SR

The length of side AC = 38.

Explanation of Solution

Given Information:

  $\begin{array}{l}BA=BC\\ \angle \text{BDC}=\angle \text{BDA}=90°\end{array}$

Figure:

  

Solution:

  $\begin{array}{l}\text{Now,}\\ \text{In ΔBAD\&ΔBCD}\\ \text{BD = BD}\left(\text{Common Side}\right)\\ \text{BA = BC}\left(\text{Given}\right)\\ \angle \text{BDA}=\angle \text{BDC}=90°\left(\text{Given}\right)\\ \Rightarrow \Delta \text{BAD}\cong \Delta \text{BCD}\left(\text{By RHS Congruency}\right)\\ \Rightarrow \text{AD = CD}\left(\text{By c}\text{.p}\text{.c}\text{.t}\right)\\ \Rightarrow \text{D is the Mid Point}\\ \Rightarrow \left(5x-6\right)=\left(3x+4\right)\\ \Rightarrow 5x-3x=4+6\\ \Rightarrow 2x=10\\ \Rightarrow x=\frac{10}{2}\\ \Rightarrow x=5\end{array}$

Thus,

  $\begin{array}{l}\text{AD}=5x-6\\ \Rightarrow 5\left(5\right)-6\\ \Rightarrow 25-6\\ \Rightarrow \text{AD}=19\\ \text{Similarly,}\\ \text{DC}=3x+4\\ \Rightarrow 3\left(5\right)+4\\ \Rightarrow 15+4\\ \Rightarrow \text{DC}=19\end{array}$

Therefore,

AC = 38.