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15 unit circles are inscribed in an equilateral triangle in such a way that each circle is externally tangent to its neighbors. What is the area of the triangle?

 

 Feb 4, 2021
 #1
avatar+128 
+1

i believe this question has already been answered here:

https://web2.0calc.com/questions/help_82190 :)

 Feb 4, 2021
 #2
avatar+268 
+6

This question...is hard!!! 

IhaveOBJD  Feb 4, 2021
 #3
avatar+118470 
+2

The  length  of  one side =   2sqrt (3)  +  8     =   sqrt (12) + 8

 

So....the  area   =    (1/2)  (sqrt (12) + 8)^2  sin (60°)   =

 

(1/2)  (sqrt (3) / 2 )  [  12 + 16sqrt (12) + 64)  =

 

[sqrt (3) /4]  [ 76 + 16sqrt (12) ]  =

 

[sqrt (3)/ 4 ] [ 76  + 32 sqrt (3) ]  =

 

[76 sqrt (3)   +  32 * 3  ]  /  4   =

 

19sqrt (3)  +  24  ≈    56.91  units^2

 

 

cool cool cool

 Feb 4, 2021
 #4
avatar+268 
+6

😳😳😳😶😶😶🤔🤔🤩🤩

.
 Feb 4, 2021

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