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Question

In ΔABC, D,E,F are respectively the midpoints of the sides AB,BC and AC.Find Area of ΔDEFArea of ΔABC.

A
2:1
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B
3:4
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C
2:3
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D
1:4
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Solution

The correct option is D 1:4Given in △ABC D,E,F are the mid points of sides AB,BC and CA respectivelyNow using mid point theorem line segment joining the mid points of two sides is parallel to third side and also half of it.∴DF=12BC⇒DFBC=12 ....(i)Similarly DEAC=12 ....(ii)EFAB=12 ....(iii)Using (i), (ii) and (iii), we haveDFBC=DEAC=EFAB=12∴△ABC∼△DEFNow if triangles are similar then ratio of their areas is equal to ratio of square of their corresponding sides.ar(△DEF)ar(△ABC)=(12)2=14

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