Question

If the area of a ∆ABC is 96 sq. unit and the radius of the escribed circles are respectively 8, 12 and 24. Find the perimeter of ∆ABC.

Answer 1

∵ ∆ = 96 sq. unit 

r₁ = 8, r₂ = 12 and r₃ = 24

∴ adding equations (i), (ii) & (iii), we get

3s – (a + b + c) = 24 

s = 24 

∴ perimeter of ∆ABC = 2s = 48 unit.