Question

Sides of triangle are given as three consecutive integers and inradius is 4 cm find area

Answer 1

Answer:

Step-by-step explanation:

let the sides are a=a, b=a-1 and c=a+1

inradius = r = ∆/s

s = (a+a+1+a-1)/2 = 3a/2

∆ = ✓[s(s-a)(s-b)(s-c)]

r = ✓[(a-2)(a+2)/12]

12×4×4 = a×a - 4

a = 14

∆ = ✓[3a²÷4(a²÷4 - 1)]

= ✓[3×14×14÷4(196÷4 - 1)]

= ✓[28224]

= 168 sq unit