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.

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Solution

The correct option is A

The two triangles $Δ$ AEF and $Δ$ DFC are congruent.

So it is equivalent to find the ratio of $Δ$ AEF to that of $Δ$ EBC -

$Δ$ AEF $\sim Δ$ EBC

AF = $\frac{1}{2}$ BC

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

$\frac{A r e a o f Δ E A F}{A r e a o f Δ E B C}$ = $\frac{1}{4}$

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