Radius of the circle

A triangle with sides 30m, 40m, and 50m is an enlarged 3-4-5 triangle. And it is a right triangle.

$A = \frac{1}{2}$ ) $bh$ $= 0.5*30*40 = 600 m^2$

$P = 30 + 40 + 50 = 120 m$

$r =$ $\frac{2A}{P}$ $=$ $\frac{2*600}{120}$ $= 10m$

The given triangle is a right triangle. The radius of the inscribed circle is given by $r=\dfrac{2A}{P}$ where $A$ is the area and $P$ is the perimeter of the triangle. So the radius is

$r=\dfrac{2\left(\dfrac{1}{2}\right)(30)(40)}{30+40+50}=\boxed{10~\text{m}}$