Question

ABC is a triangle in which ∠A =90°, AN⊥ BC, BC = 12 cm and AC = 5cm. Find the ratio of the areas of ΔANC and ΔABC.

Answer 1

In ΔANC and ΔABC

∠C = ∠C                         [Common]

∠ANC = ∠BAC                 [Each 90°]

Then, ΔANC ~ ΔBAC         [By AA similarity]

By area of similarity triangle theorem

`("Area"(triangleANC))/("Area"(triangleBAC))="AC"^2/"BC"^2`

`=5^2/12^2`

`=25/144`