A triangular park has sides of 25 m, 39 m and 56 m. A circular fountain of the largest possible size is to be built inside it, just touching all three sides. What is the radius of the fountain, in metres?

The largest circle that fits inside a triangle is its inscribed circle, whose radius is $r$ = area/$s$, where $s$ is the SEMI-perimeter. Here $s=(25+39+56)/2=60$, and Heron'$s$ formula gives area = √$(60\times 35\times 21\times 4)$ = √176400 = 420 sq m. So $r=420/60=7$ m. The trap 3.5 divides by the full perimeter 120 instead of the semi-perimeter; 14 uses 2 $x$ area/$s$, doubling the correct value; 60 quotes the semi-perimeter itself as though it were a radius.