Question

In a right angled $\Delta$ABC right angled at B, AD is the angular bisector of angle A. If the ratio of AB:BD = 2:1. Find the length of the hypotenuse if AB = 2 m.

• A. (10/3) m
• B. (5/3) m
• C. 5 m
• D. 8 m

Answer 1

The correct option is A

(10/3) m

The angular bisector divides the line segment joining the angle and the opposite side in the ratio of the sides containing the angle.
$\frac{AB}{AC}=\frac{BD}{DC}$
$\frac{AB}{BD}=\frac{AC}{CD}$
$\frac{AC}{CD}$ =2(since~AB:BD=2:1)
Let CD = x m
AC=2x m.
Using Pythagoras theorem in $\Delta$ ABC,
$A{B}^2+B{C}^2=A{C}^2$
$4+(1+x{)}^2=4x^2$
Solving the above equation, we get
$x=\frac{5}{3}$
$AC=\frac{10}{3}m$