Question

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

Answer 1

C

Explanation:

60

Answer 2

ΔADB is a right triangle at ∠D

So, AB ⇒ Hypotenuse & AD,DB ⇒ Legs

∴
`AD = √(AB^2 - DB^2) = √(20^2 - 16^2)=√(400-256) =√(144) =12`

ΔADC is a right triangle at ∠D

So, AC ⇒ Hypotenuse & AD,DC ⇒ Legs

`CD = √(AC^2 - DC^2) = √(15^2 - 12^2)=√(225-144) =√(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