Question

In triangle ABC, AD = DB , DE is parallel to BC, and the area of triangle ABC is 40. What is the area of triangle ADE ?

A. 10
B. 15
C. 20
D. 30
E. it cannot be determined from the information given

Answer 1

Since DE is parallel to BC, hence △ABC is similar to △ADE. Now since, AD=DB=>B=2AD=>altitude from A to DE is half of altitude from A to BC and BC=2DE. Given, Area(△ABC)=40=>2(⊥fromAtoBC)(BC)=40=>12/2∗⊥(fromAtoDE)(2∗DE)=40=>1/2(⊥fromAtoDE)(DE)=10.

That means that the area for △ADE=10.