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.
The two triangles ΔAEF and ΔDFC are congruent.
So it is equivalent to find the ratio of ΔAEF to that of ΔEBC -
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