There is a triangular field in front of a classroom. The two sides which are perpendicular measures 6 m and 8 m. The teacher told students to construct a circular flower bed which touches the three sides of the field. Find the radius of circular flower bed. What values are developed in the students through this activity.



The perpendicular sides of the triangle are 6 m and 8 m
Therefore, the third side, hypotenuse is 10 m (By Pythagorean theorem)
We also know that, the inradius of the circle is the ratio between its area and the semi-perimeter
r = Δ/s

ARea of the triangle = 1/2 * 6 * 8 = 24 sq m
semi-perimeter, s = (6+8+10)/2 = 12 m
So, r = 24/12 = 2 m