A triangle has sides with lengths of 4, 9, and 7. What is the radius of the triangles inscribed circle?

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Answer 1 · 2016-01-27T14:35:27

$Radius=(3sqrt5)/5$

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, $s=(4+9+7)/2=20/2=10$

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

$rarrArea=sqrt(10(10-4)(10-9)(10-7))$

$Area=sqrt(10(6)(1)(3))$

$Area=sqrt(10(18))$

$Area=sqrt180=6sqrt5$

$Radius=A/s=(6sqrt5)/10=(3sqrt5)/5$