Question

In figure, ∠ABC = 90°, AD = 15 cm and DC = 20 cm. If BD is the bisector of ∠ABC, then perimeter of ΔABC is ______.

Answer 1

In figure, ∠ABC = 90°, AD = 15 cm and DC = 20 cm. If BD is the bisector of ∠ABC, then perimeter of ΔABC is 84 cm.

Explanation:

By the Angle Bisector Theorem, `(AD)/(DC) = (AB)/(BC)`. 

So `(AB)/(BC) = 15/20 = 3/4`.

Let AB = 3k and BC = 4k.

Then AC = AD + DC

= 15 + 20

= 35

= 5k

So k = 7.

Thus AB = 21 cm, BC = 28 cm, AC = 35 cm.

Perimeter = 21 + 28 + 35

= 84 cm