SOLUTION: PLEASE HELP!! Show that an equilateral triangle with area A has sides of length 2squarerootA/3^(1/4).

Question 279110: PLEASE HELP!!
Show that an equilateral triangle with area A has sides of length 2squarerootA/3^(1/4).
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the sides of the triangle be S.
The area of a triangle is

In this case,

Now we need to find H.
Draw it out.
The distance from the top vertex to the middle of the base is the height, H.
It forms a right triangle with one leg, H, the other leg, S/2, and the hypotenuse, S.
Use the Pythagorean theorem to find H in terms of S.

Then from the area formula,

Then moving those terms around.

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