Question

If D is a point on the side AB of ΔABC such that AD : DB = 3 : 2 and E is a point on BC such that DE || AC. Find the ratio of areas of ΔABC and ΔBDE.

Answer 1

We have,

`"AD"/"DB"=3/2`

`rArr"DB"/"AD"2/3`

In ΔBDE and ΔBAC

∠B = ∠B                                  [common]

∠ BDE = ∠A                             [corresponding angles]

Then, ΔBDE ~ ΔBAC                [By AA similarity]

By area of similar triangle theorem

`("area"(triangleABC))/("area"(triangleBDE))="AB"^2/"BD"^2`

`=5^2/2^2`                             `["AD"/"DB"=3/2]`

`=25/4`