Question

ABC is a right-angled triangle, right-angled at B. D is a point on AC such that AD = 12 cm and CD = 16 cm. If BD bisects ∠ABC , then the perimeter of ΔABC will be:
1. 67.2 cm
2. 56.2 cm
3. 66.2 cm
4. 66 cm

Answer 1

Correct Answer - Option 1 : 67.2 cm

Given:

AD = 12 cm and CD = 16 cm

Calculation:

BD is angle bisector of ∠ABC.

⇒ AD/CD = AB/BC

⇒ AB/BC = 12/16 = 3/4

Let AB and BC be 3a and 4a respectively.

Using pythagoras theorem,

⇒ AC² = AB² + BC²

⇒ AC = 5a

⇒ AD + DC = AC

⇒ AC = 12 + 16 = 28

⇒ 28 = 5a

⇒ a = 5.6

∴ Perimeter of ΔABC = 3a + 4a + 5a = 12a = 67.2 cm