Question 70177

http://mcraefamily.com/MathHelp/GeometryTriangleCenterInscribedCircle2.htm

This site describes a formula that I did not know till I went looking for it.

radius = (Area of the circle)/s, where s=(1/2)(sum of the sides)

For your problem Area = (1/2)3*4=6 sq inches.
(sum of sides)/2 = 12/2=6
So r=6/6= 1 inch

Cheers,
Stan H.