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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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