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

Jan 31, 2016

$R a \mathrm{di} u s = 1.006 \ldots$

#### Explanation:

Radius of circle inscribed in a triangle$= \frac{A}{s}$

Where,

$A$=Area of triangle,

$s$=Semi-perimeter of triangle$= \frac{a + b + c}{2}$ Note $a , b , c$ are sides of the triangle

So,$s = \frac{4 + 6 + 9}{2} = \frac{19}{2} = 9.5$

We can find the area of triangle using Heron's formula:
Heron's formula:
$A r e a = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

$\rightarrow A r e a = \sqrt{9.5 \left(9.5 - 4\right) \left(9.5 - 6\right) \left(9.5 - 9\right)}$

$A r e a = \sqrt{9.5 \left(5.5\right) \left(3.5\right) \left(0.5\right)}$

$A r e a = \sqrt{9.5 \left(9.625\right)}$

$A r e a = \sqrt{91.43} = 9.562$

$R a \mathrm{di} u s = \frac{A}{s} = \frac{9.562}{9.5} = 1.006 \ldots$