+77 Find the inradius of $\triangle JKL$ if $JK=JL=17$ and $KL = 16$.
+128407
The inradius is given by :
2A / P where A is the area and P is the perimeter
The perimeter is easy = 16 + 2*17 = 16 + 34 = 50
The triangle is isosceles.....let the base =16
And the height can be found using the Pythagorean Theorem as
√ [17^2 - 8^2] = √ [289 - 64] = √ 225 = 15
So....the area = (1/2)B*H = (1/2) 16 * 15 = 120
So.......the inradius is 2 * 120 / 50 = 240 / 50 = 24/5 = 4.8
Here's a pic.....AB is the inradius
