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Let ABC be any triangle. Equilateral triangles BCX, ACY, and BAZ are constructed such that none of these triangles overlaps triangle ABC. The perimeter of hexagon AZBXCY is 78. What is the perimeter of ABC?

https://latex.artofproblemsolving.com/4/4/c/44c8b7bd5ee68a800c23ac75ba1c3ee7781042ec.png

 Oct 1, 2019
 #1
avatar+104962 
+2

Since all of the triangles bordering ABC are equilateral....then the perimeter of the hexagon can be expressed as :

 

2 (CB) + 2 (CA) + 2 (AB)  =  78

 

2 ( CB + CA + AB)   =  78      divide both sides by 2

 

(CB + CA + AB)  =  39

 

(perimeter of triangle ABC)  = 39

 

 

cool cool cool  

 Oct 1, 2019

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