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Question

If D, E, F are the midpoints of sides BC, CA and AB of â–³ ABC, then the ratio of the area of â–³ DEF to â–³ ABC is:


A

1: 4

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B

1: 2

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C

2: 3

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D

4: 5

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Solution

The correct option is A

1: 4


D, E, F are the midpoints of sides BC, CA and AB of ABC ...(given)

Hence, DEAB=FEBC=FDAC=12 .... (SSS Similarity)

DEF ABC

area (Δ DEF)area (Δ ABC)=(DFAC)2=(12)2=14


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