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Question

In the figure given below AB = 3 cm, AC = 5 cm and AD = 4 cm and D is the midpoint of BC. Then the length of BD is :


A

1 cm

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B

2 cm

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C

4 cm

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D

3 cm

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Solution

The correct option is A

1 cm


Since D is the mid-point of BC,

From Apollonius theorem,

AB2+AC2=2(BD2+AD2)32+52=2(BD2+42)(9+252)=BD2+16 BD2=1716 BD=1 cm.


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