Question

In the adjoining figure, DE is parallel to BC and AD = 1 cm, BD = 2 cm. What is the ratio of the area of ∆ABC to the area of ∆ADE?

Answer 1

GIVEN: DE is parallel to BC, AD = 1cm and BD = 2cm.

TO FIND: Ratio of ΔABC to area of ΔADE

According to BASIC PROPORTIONALITY THEOREM, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

In ΔABC, DE || BC.

`(AD)/(AB)=(AE)/(AC)`

`1/(2+1)=(AE)/(AC)`

`⇒ (AE)/(AC)=1/3`

So

`(ar(Δ ABC))/(ar(Δ ADE)``=((AC)/(AE))^2`

`=(3/1)^2`

`=9/1`