Question

If ∆ABC and ∆DEF are two triangles such that \[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}\], then write Area (∆ABC) : Area (∆DEF).

Answer 1

GIVEN: ΔABC and ΔDEF are two triangles such that.

\[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}\]

TO FIND: Area (ABC) : Area (DEF)

We know that two triangles are similar if their corresponding sides are proportional.

Here, ΔABC and ΔDEF are similar triangles because their corresponding sides are given proportional, i.e. \[\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = \frac{3}{4}\]

Since the ratio of the areas of two similar triangle is equal to the ratio of the squares of their corresponding sides.

`⇒ (Area(Δ ABC))/(Area(Δ DEF))=9/12`