A triangle has sides with lengths of 4, 6, and 9. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-01-31T09:12:07

$Radius=1.006...$

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, $s=(4+6+9)/2=19/2=9.5$

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

$rarrArea=sqrt(9.5(9.5-4)(9.5-6)(9.5-9))$

$Area=sqrt(9.5(5.5)(3.5)(0.5))$

$Area=sqrt(9.5(9.625))$

$Area=sqrt91.43=9.562$

$Radius=A/s=9.562/9.5=1.006...$