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Find the inradius of $\triangle JKL$ if $JK=JL=17$ and $KL = 16$.

 Jul 14, 2017
 #1
avatar+94619 
+2

 

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

 

 

cool cool cool

 Jul 14, 2017

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