Question

The side of triangle are consecutive integars inradius is 4 find area of .

Answer 1

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

hope it helps you