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**+2 **

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

CPhill
Mar 20, 2018