Answer: [tex]2\sqrt{2}[/tex]
Step-by-step explanation:
The inradius is given by the area of the triangle divided by the semiperimeter.
The semiperimeter is [tex]\frac{12+12+8}{2}=16[/tex].
Thus, by Heron's formula, the area is [tex]\sqrt{16(16-12)(16-12)(16-8)}=32\sqrt{2}[/tex].
Therefore, the radius is [tex]\frac{32\sqrt{2}}{16}=2\sqrt{2}}[/tex]
