A triangle has sides with lengths of 7, 7, and 6. What is the radius of the triangles inscribed circle?

Jan 26, 2016

If $a , b \mathmr{and} c$ are the three sides of a triangle then the radius of its in center is given by

$R = \frac{\Delta}{s}$

Where $R$ is the radius $\Delta$ is the are of the triangle and $s$ is the semi perimeter of the triangle.

The area $\Delta$ of a triangle is given by

Delta=sqrt(s(s-a)(s-b)(s-c)

And the semi perimeter $s$ of a triangle is given by
$s = \frac{a + b + c}{2}$

Here let $a = 7 , b = 7 \mathmr{and} c = 6$

$\implies s = \frac{7 + 7 + 6}{2} = \frac{20}{2} = 10$

$\implies s = 10$

$\implies s - a = 10 - 7 = 3 , s - b = 10 - 7 = 3 \mathmr{and} s - c = 10 - 6 = 4$

$\implies s - a = 3 , s - b = 3 \mathmr{and} s - c = 4$

$\implies \Delta = \sqrt{10 \cdot 3 \cdot 3 \cdot 4} = \sqrt{360} = 18.9736$

$\implies R = \frac{18.9736}{10} = 1.89736$ units

Hence, the radius of inscribed circle of the triangle is $1.89736$ units long.