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I need help with this question please, thank you. 

 

 Jun 7, 2019
 #1
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See the following image :

 

ED  = r

Angle HEF  = 120°     so angle DEF = 60°

And angle EDF  = 90°

And angle EFD = 30°

So triangle EDF is a 30 - 60 -90 right triangle  with ED = r, DF = √3 r  and EF = 2r

 

The area  of the smaller  equilateral triangle  = 3(1/2)(ED)^2* sin (120°)  =  3(1/2)(r)^2(√3 / 2) 

The area of the larger equilateral triangle = 3(1/2) (EF)^2  * sin (120°) = 3(1/2) (2r)^2 (√3 / 2)

 

So we have that

 

(3√3)/4 * [ (2r)^2 - r^2]  = 36

 

(3√3)/4 * [ 4r^2 - r^2 ] = 36        multiply through by 4

 

3√3 [ 3r^2]  =  144        

 

9√3 r^2  =  144

 

r^2  =  144 / (9√3)

 

r^2  =  16/ √3

 

r =   4 / 4√3   cm  ≈  3.04 cm

 

 

cool cool cool

 Jun 7, 2019
edited by CPhill  Jun 7, 2019

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