Find the diameter of the incircle for a triangle whose side lengths are 8, 15, and 17.
The formula for the radius of an inscribed circle in a triangle is 2 * Area= Perimeter * Radius. In an 8, 15, 17 right triangle, twice the area is 8 * 15= 120 and the perimeter is 8+15+17= 40. So the radius is 120/40=3. The radius is half the diameter so your answer is 3 * 2= 6.
I do not know that formula so here is my method.
The radius is r units. The encircle centre is the point (r,r)
To find r, the perpendicular distance of the hypotenuse to (r,r) must equal r.
r=|Ax1+By1+C|√A2+b2r=|8r+15r−120|√82+152r=|23r−120|17r=120−23r1717r+23r=12040r=120r=3
Radius is 3
Diameter is 6