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Question

Given a square ABCD such that line joining C and the midpoint of AD i.e. F meets line joining AB at E when extended. Find the ratio of area of Δ DFC to that of Δ EBC.

 



Correct Answer
A

1/4

Your Answer
B

1/2

Your Answer
C

1/5

Your Answer
D

1/6

Your Answer
E

1/7


Solution

The correct option is A

1/4


The two triangles ΔAEF and ΔDFC are congruent.

So it is equivalent to find the ratio of ΔAEF to that of ΔEBC -

Δ AEFΔEBC

AF = 12 BC

The ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Area of Δ EAFArea of Δ EBC = 14

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