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How do you find the side of an equilateral triangle whose area is 36 radical 3?
Wiki User
∙ 14y ago
Suppose the sides of the triangle are 2x.
Drop a perpendicular bisector from the apex to the base. Now consider the half-triangle formed.
The hypotenuse is one of the sides of the original triangle, so 2x in length.
The base is half the side of the original traiangle, so x in length.
So, by Pythagoras, the height2 is (2x)2 - x2 = 3*x2
So height = x*sqrt(3)
Then area of the whole traiangle = base*height/2 = 2x*x*sqrt(3)/2
=x2*sqrt(3)
This is given as 36*radical 3 so x2 = 36 ie x = 6
So the sides, = 2x = 12 units.
Wiki User
∙ 14y ago
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