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

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Answer 1 · 2016-01-26T18:31:46

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

$R=Delta/s$

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
$s=(a+b+c)/2$

Here let $a=7, b=7 and c=6$

$implies s=(7+7+6)/2=20/2=10$

$implies s=10$

$implies s-a=10-7=3, s-b=10-7=3 and s-c=10-6=4$

$implies s-a=3, s-b=3 and s-c=4$

$implies Delta=sqrt(10*3*3*4)=sqrt360=18.9736$

$implies R=18.9736/10=1.89736$ units

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