Question

Geometry question! Help!

Answer 1

Answer: $2\sqrt{2}$

Step-by-step explanation:

The inradius is given by the area of the triangle divided by the semiperimeter.

The semiperimeter is $\frac{12+12+8}{2}=16$.

Thus, by Heron's formula, the area is $\sqrt{16(16-12)(16-12)(16-8)}=32\sqrt{2}$.

Therefore, the radius is $\frac{32\sqrt{2}}{16}=2\sqrt{2}}$