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The perimeter of a triangle is 12 and its inradius is 1. What is the area of the triangle

 Nov 14, 2018
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This is a little easier than you might realize

 

Let us call the sides AB, BC   and AC

 

And call the center of the incircle  O

 

So....we can divide the larger triangle into three separate triangles  - AOB, BOC  and AOC

 

The inradius of the incircle forms an altitude of each triangle since it is perpendicular to each side

 

So.....the  area, A,  of the larger triangle can be expressed  as

 

A = (1/2)  [ altitude * ( sum of the bases ) ]  = 

 

(1/2) [ (1) * perimeter ]  =

 

 (1/2)  [ (1)(AB + BC + AC ) ]  =

 

(1/2) [ 1 * 12 ]  =

 

(1/2) [ 12]  =

 

6 units^2

 

 

cool cool cool

 Nov 14, 2018

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