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Question Image

G is the centroid of △ABC. GE and GF are drawn parallel to AB and AC respectively. Find ar( △GEF) : ar( △ABC).


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a

1:9

b

1:3

c

1:16

d

1:4  

answer is A.

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Detailed Solution

Given that △ABC, GE∥ABand GF∥AC.
Question ImageDraw a median AD.
Since, G is the centroid.
We know, GDAD=13(Centroid divided the median in the ratio of 2 : 1)
Ratio of areas of the triangle is equal to the ratio of the square of medians.
Thus, A(△GEF)A(△ABC)=GD2AD2 ⇒A(△GEF)A(△ABC)=19 .
Therefore, A( △GEF) : A( △ABC) is 1:9.
Hence option 1 is the answer.
 
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