What is the radius of the inscribed circle of a triangle with side lengths 9, 13, and 14? Express answer in simplest radical form.

√10

Step-by-step explanation:

The radius of the incircle of a triangle is:

r = √ (s (s-a) (s-b) (s-c)) / s

where s is half the perimeter, s = (a + b + c) / 2.

s = (9 + 13 + 14) / 2

s = 18

r = √ (18 (18-9) (18-13) (18-14)) / 18

r = √ (18 * 9 * 5 * 4) / 18

r = √10