Question

In the given figure, DE || BC, AD = 1 cm and BD = 2 cm. What is the ratio of the ar (ΔABC) to the ar (ΔADE)?

Answer 1

It is given that AD = 1 cm, BD = 2 cm and DE || BC

In ΔADE and ΔABC

∠ADE = ∠ABC (Corresponding angles)

∠A = ∠A (Common angle)

By AA similarity

ΔADE ∼ ΔABC

Ratio of area of similar triangles is equal to the square of the ratio of corresponding sides.

∴ `("ar"(Δ"ABC"))/("ar"(Δ"ADE")) = ("AB"^2)/("AD"^2)`

⇒ `("ar"(Δ"ABC"))/("ar"(Δ"ADE")) = (3^2)/(1^2)`

⇒ `("ar"(Δ"ABC"))/("ar"(Δ"ADE")) = (9)/(1)`

Therefore, the ratio of the ar (ΔABC) : ar (ΔADE) is 9 : 1.