SOLUTION: Please help me solve this question! Here are the directions: Find the radius of the circle inscribed in the triangle. (its an isosceles triangle and the longer sides have a m

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Question 192085This question is from textbook Geometry
: Please help me solve this question!
Here are the directions:
Find the radius of the circle inscribed in the triangle.
(its an isosceles triangle and the longer sides have a measurement of 12 and the last smallest side has a measurement of 8)
Now, I know the answer is 2 sqrt ( 2 )
but i need to know what are the steps to getting the answer? please help!! This question is from textbook Geometry

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


Finding for "Radius" inscribed in a triangle:
Working Eqn:
Radius = Area%5BT%5D%2Fk= sqrt%28k%28k-a%29%28k-b%29%28k-c%29%29%2Fk, * See properties of Triangle


But solving for "k":
We know an Isosceles Triangle has 2 equal sides, a=b=12, and the other side, c=8:

k=%281%2F2%29%28a%2Bb%2Bc%29=%281%2F2%29%2812%2B12%2B8%29=32%2F2=red%2816%29


Subst. in our Working Eqn:


R=sqrt%288%29=sqrt%284%2A2%29=sqrt%284%29%2Asqrt%282%29
red%28R=2%2Asqrt%282%29%29, Answer

Thank you,
Jojo