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Question

In a right angled ΔABC 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

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B

(5/3) m

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C

5 m

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D

8 m

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Solution

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.
ABAC=BDDC
ABBD=ACCD
ACCD =2(since~AB:BD=2:1)
Let CD = x m
AC=2x m.
Using Pythagoras theorem in Δ ABC,
AB2+BC2=AC2
4+(1+x)2=4x2
Solving the above equation, we get
x=53
AC=103m


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