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You could also use instead of Pythagoras the 30:60:90 rule to get a = sqrt(3)*x/6 = x / (2*sqrt(3))

KarishmaB
BDSunDevil
is there any other way solving the problem without using the area-formula for equilateral triangle?

If you don't know the equilateral triangle area formula, you will need to use the area formula for any triangle i.e. (1/2)*base*altitude
You will get the area for the equilateral triangle.

Since perimeter = x meters, length of side = x/3 meters.

So base = x/3
What about the altitude? You need to use pythagorean theorem to figure it out. The altitude bisects the opposite side in an equilateral triangle so
(x/3)^2 = (x/6)^2 + altitude^2
altitude =\(x/(2\sqrt{3})\)

Area of triangle = \((1/2)*(x/3)*(x/(2\sqrt{3}) = x^2/12*\sqrt{3}\)

This is the same as the formula (obviously!)\(\sqrt{3}/4 * (x/3)^2 = x^2/12*\sqrt{3}\)
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