A triangle has sides with lengths of 8, 4, and 6. What is the radius of the triangles inscribed circle?

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Answer 1 · 2018-06-06T14:42:36

$r = \frac{\sqrt{15}}{3} \approx 1.29$ $r=(sqrt15)/3 ~~1.29$

Here is the formula for a triangle inscribed circle:

$s = \frac{a + b + c}{2}$ $s = (a+b+c)/2$

$r = \sqrt{\frac{(s - a) (s - b) (s - c)}{s}}$ $r = sqrt(((s-a)(s-b)(s-c))/s)$

Plug in our values:

$s = \frac{8 + 4 + 6}{2}$ $s = (8+4+6)/2$

$s = 9$ $s=9$

$r = \sqrt{\frac{(9 - 8) (9 - 4) (9 - 6)}{9}}$ $r = sqrt(((9-8)(9-4)(9-6))/9)$

$r = \sqrt{\frac{5}{3}}$ $r=sqrt(5/3)$

$r = \frac{\sqrt{15}}{3} \approx 1.29$ $r=(sqrt15)/3 ~~1.29$