Question

In the following figure, DE || BC. If DE = 4 cm, BC = 8 cm and Area (ΔADE) = 25 cm², find the area of ΔABC.

Answer 1

We have, DE || BC, DE = 4 cm, BC = 8 cm and area (ΔADE) = 25cm²

In ΔADE and ΔABC

∠A = ∠A [Common]

∠ADE = ∠ABC [Corresponding angles]

Then, ΔADE ~ ΔABC [By AA similarity]

By area of similar triangle theorem

`("Area"(triangleADE))/("Area"(triangleABC))="DE"^2/"BC"^2`

`rArr25/("Area"(triangleABC))=4^2/8^2`

⇒ Area (ΔABC) = `(25xx64)/16=100  "cm"^2`