Question

The perimeter of triangle ABC is _____. A. 51 B. 55 C. 60 D. 68

Answer 1

ΔADB is a right triangle at ∠D

So, AB ⇒ Hypotenuse & AD,DB ⇒ Legs

∴ $AD = \sqrt{AB^2 - DB^2} = \sqrt{20^2 - 16^2}=\sqrt{400-256} =\sqrt{144} =12$

ΔADC is a right triangle at ∠D

So, AC ⇒ Hypotenuse & AD,DC ⇒ Legs

$CD = \sqrt{AC^2 - DC^2} = \sqrt{15^2 - 12^2}=\sqrt{225-144} =\sqrt{81} =9$

∴ BC= BD+ DC = 16 + 9 = 25

∴ The perimeter of triangle ABC = AB + BC + CA = 20 + 25 + 15 = 60.

So, The correct answer is option  C. 60