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

 

2.  is the incenter of Triangle ABC. We have CE=12, AE=9, and AB=12. Find BC.

 Nov 11, 2019
 #1
avatar+106027 
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Why would you put both these question on one post?

That makes no sense to me.

 Nov 11, 2019
edited by Melody  Nov 11, 2019
 #2
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1. We can assume that the triangle is equilateral, so the area is sqrt(3)/4*(12/2)^2 = 9 sqrt(3).

 

2. From similar triangles, BC = (12 + 12)/(12 + 9)*12 = 96/7.

 Nov 11, 2019
 #3
avatar+105411 
+1

 

The inradius  is the height of three smaller triangles with the sum of their bases = the perimeter of the large triangle

 

So.....the area of the large triangle is

 

(1/2) (perimeter) ( 1)  =

 

(1/2) (12) * 1  =

 

6 units^2

 

 

cool cool cool

 Nov 11, 2019
 #4
avatar+105411 
+1

Second one

 

The incenter  is the point where the angle  bisectors meet

 

Therefore  BE  is an angle bisector.....so we have the relationship that

 

AB / AE  =  BC  / EC

 

12 / 9  =  BC  / 12    cross-multiply

 

12 * 12  =  BC * 9

 

12 * 12 / 9  = BC

 

144 / 9  =  BC   =   16

 

 

cool cool cool

 Nov 11, 2019

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