Question

If ∆ABC and ∆DEF are two triangles such that $\frac{\mathrm{AB}}{\mathrm{DE}}=\frac{\mathrm{BC}}{\mathrm{EF}}=\frac{\mathrm{CA}}{\mathrm{FD}}=\frac{2}{5}$, then Area (∆ABC) : Area (∆DEF) =

(a) 2 : 5
(b) 4 : 25
(c) 4 : 15
(d) 8 : 125

Answer 1

Given: ΔABC and ΔDEF are two triangles such that .

To find:

We know that if the sides of two triangles are proportional, then the two triangles are similar.

Since , therefore, ΔABC and ΔDEF are similar.

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

Hence the correct answer is .