You could also use instead of Pythagoras the 30:60:90 rule to get a = sqrt(3)*x/6 = x / (2*sqrt(3))
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!)\(\sqrt{3}/4 * (x/3)^2 = x^2/12*\sqrt{3}\)