Question

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

Answer 1

DE || BC

ΔADE ΔABC                                 [By AA similarity]

`∴ (ar (DeltaABC))/(ar(DeltaADE)) = (AB^2)/(AD^2)`         [By area similarity theorem]

`⇒ (ar (DeltaABC))/(ar(DeltaADE)) = 3^2/1^2`

`⇒ (ar (DeltaABC))/(ar(DeltaADE)) = 9/1`