A triangle has sides with lengths of 3, 5, and 4. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-01-31T09:03:03

$1$

Radius of circle inscribed in a triangle $=A/s$

Where,

$A$ =Area of triangle,

$s$ =Semi-perimeter of triangle $=(a+b+c)/2$ Note $a,b,c$ are sides of the triangle

So, $s=(3+5+4)/2=12/2=6$

We can find the area of triangle using Heron's formula:
Heron's formula:
$Area = sqrt(s(s-a)(s-b)(s-c))$

$rarrArea=sqrt(6(6-3)(6-5)(6-4))$

$Area=sqrt(6(3)(1)(2))$

$Area=sqrt(6(6))$

$Area=sqrt36=6$

$Radius=A/s=6/6=1$