Question

In figure, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then PD = ______ and CD = ______.

Answer 1

In figure, if ∠A = ∠C, AB = 6 cm, BP = 15 cm, AP = 12 cm and CP = 4 cm, then PD = 5 cm and CD = 2 cm.

Explanation:

Triangles ABP and CDP are similar (∠A = ∠C and ∠APB = ∠CPD).

So `(AB)/(CD) = (BP)/(PD) = (AP)/(CP)`. 

Since `(AP)/(CP) = 12/4 = 3`, we have

`6/(CD) = 3`

⇒ CD = 2 cm

And `15/(PD) = 3`

⇒ PD = 5 cm