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Even if you answer one of them  thank you 

 Apr 14, 2019
 #1
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First one.....the area of the inscribed equilateral triangle  =

 

3(1/2)r^2 sin  120  =  ( 3√3/4) r^2

 

The Height of the circumscribed equilateral triangle = 3r

 

And we  can find the base as

 

tan 60 = 3r /(1/2) Base

√3 =6r / Base

Base = 6r/√3  = 2√3r

So....the area of the circumscribed eqilateral triangle is  (1/2)Base* Height  = (1/2)2√3r * 3r =  3√3r^2

 

So we have that

 

Area of circumscribed triangle - Area of inscribed triangle =  36

 

(3√3  - 3√3/4) r^2  = 36

3(√3 -  √3/4) r^2 = 36

  (√3 -  √3/4)r^2  = 12

 

r^2  =  12 / ( √3 - √3/4 )  

 

r = √ [  12 / ( √3 - √3/4 ) ] ≈  3.04 cm

 

 

cool cool cool

 Apr 14, 2019

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