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The exact amount of fencing that enclosed the four congruent equilateral triangular corrals shown here is reused to form one large equilateral triangular corral. What is the ratio of the total area of the four small corrals to the area of the new large corral? Express your answer as a common fraction.
 

tertre  Mar 20, 2018
 #1
avatar+89775 
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We have  12 equal sides  in the 4 triangles

 

Let s  =  the side of each

 

The total area is     4 (1/2)(s^2)√3/2   =  √3s^2

 

 

So....in a larger equilateral triangle.....each  side  will be  12s/3  =  4s   

 

So....the area of the largwer equilateral triangle  =  

 

(1/2) (4s)^2 √3/2  =  16s^2√3/4   =  4√3s^2

 

So....the desired ratio is     √3s^2  / [ 4√3  s^2 ]   =   1 / 4

 

 

cool cool cool

CPhill  Mar 20, 2018
 #2
avatar+3171 
+2

Thanks so much, CPhill! Yay! smiley

tertre  Mar 20, 2018

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