Question

In the triangle ABC, BD bisects angle B and is perpendicular to AC. If the lengths of the sides of the triangle are expressed in terms of x and y as shown, find the values of x and y.

Answer 1

In $\Delta$ABD and $\Delta$CBD
BD=BD (common)
$\angle ADB=\angle CDB(each{90}^0$ )
$\angle ABD=\angle CDB$ ( BD bisects angle B)
$\Delta ABD\cong \Delta$ CDB (by a. s a)
$\to$ 3x+1=5y-2 (cpctc )
$\to x=\frac{(5y-3)}{3}$......(1)
$\to$ x+1=y+2 (cpctc)
$\to$ x=y+1. .........(2)
from (1) and (2)
$\to$ y-3=3(y+1)
$\to$ 5y-3y=3+3
$\to$ 2y=6
$\to$ y=3
put y=3 in (2)
$\to$ x=3+1
$\to$ x=4