A triangle has sides 5 cm, 12 cm and 13 cm. What is the radius of its inscribed circle?

Since $5^2+12^2=13^2$, the triangle is right-angled. For a right triangle with legs a, $b$ and hypotenuse $c$ the inradius is $r=(a+b-c)/2=(5+12-13)/2=2$ cm. Checking with area = $r\times s$: area = 30, $s=15$, so $r=30/15=2$ cm. The value 6.5 cm is the circumradius (half the hypotenuse), a common slip.