ΔADB is a right triangle at ∠D
So, AB ⇒ Hypotenuse & AD,DB ⇒ Legs
∴ [tex]AD = \sqrt{AB^2 - DB^2} = \sqrt{20^2 - 16^2}=\sqrt{400-256} =\sqrt{144} =12[/tex]
ΔADC is a right triangle at ∠D
So, AC ⇒ Hypotenuse & AD,DC ⇒ Legs
[tex]CD = \sqrt{AC^2 - DC^2} = \sqrt{15^2 - 12^2}=\sqrt{225-144} =\sqrt{81} =9[/tex]
∴ 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
