Question

The area of triangle abc is 6 square centimeters. Ab is parallel to de . Bd=4bc . What is the number of square centimeters in the area of triangle cde ?

Answer 1

It is given that area( Δ ab c) =6 square units.

Also ab║d e

⇒b d =4 b c

I have depicted picture below.

Consider Δ cde in which points a and b are in the interior such that ab║de.

So, as you know that if in a triangle line joining two points is parallel to third side then the two sides are proportional.i.e

⇒ca/ae =cb / bd

Also, ∠ c is common.

∴Δcab is similar to Δ cde.

As we know if ratio of areas of two similar triangles is  square of their corresponding sides.

 =$\frac{Ar(Δcab)}{Ar(Δcde)}=[\frac{cb}{bd}]^2$

⇒6/Δcde =1/4

⇒Ar (Δ cde)=6×4

Ar (Δ cde) =24 square centimeter