Question 1108928: find the length of each side of an equilateral triangle for which each apothem has a length of 2 cm Found 2 solutions by Alan3354, addingup:Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! find the length of each side of an equilateral triangle for which each apothem has a length of 2 cm
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The apothem is 1/3 of the altitude --> altitude = 6 cm
altitude = s^2 - (s/2)^2 = 6
s^2 - s^2/4 = 6
3s^2 = 24
s^2 = 8
s = 2sqrt(2) cm
You can put this solution on YOUR website! apothem: a
side: x
An equilateral divided by the apothem into 2 right triangles where each right triangle is a 30-60-90 triangle.
cos(30) = a/x
1/cos(30) = x/a
1/cos(30)*a = x
(1/0.866)*2 = x
x = 2.31
