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Question

# In ΔABC, D, E and F are midpoints of ¯¯¯¯¯¯¯¯AB,¯¯¯¯¯¯¯¯BC and ¯¯¯¯¯¯¯¯AC respectively. If A(ΔABC)=40 then A(ΔDEF)= ..................

A
10
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B
403
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C
20
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D
5
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Solution

## The correct option is A 10D,E and F are the mid-points of the sides ¯¯¯¯¯¯¯¯AB,¯¯¯¯¯¯¯¯BC and ¯¯¯¯¯¯¯¯CA of ΔABC.FD∥BCFD=12BC⇒FDBC=12DE∥ACDE=12AC⇒DEAC=12EF∥ABEF=12AB⇒EFAB=12∴ABC∼EDF ....... [By SSS test of similarity]The ratios of areas of similar triangles is equal to the squares of the ratio of their corresponding sides.⇒A(△DEF)A(△ABC)=(EFAB)2=(12)2⇒A(△DEF)40=14⇒A(△DEF)=10∴ Area of △DEF is 10 sq. units.

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