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

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Question 279110: PLEASE HELP!!
Show that an equilateral triangle with area A has sides of length 2squarerootA/3^(1/4).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the sides of the triangle be S.
The area of a triangle is
A=%281%2F2%29BH
In this case,
B=S
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.
S%5E2=H%5E2%2B%28S%2F2%29%5E2
H%5E2=S%5E2-%281%2F4%29S%5E2
H%5E2=%283%2F4%29S%5E2
H=%28sqrt%283%29%2F2%29S
Then from the area formula,
A=%281%2F2%29BH
A=%281%2F2%29%28S%29%28sqrt%283%29%2F2%29S
A=%28sqrt%283%29%2F4%29S%5E2
Then moving those terms around.
S%5E2=4A%2Fsqrt%283%29
S=%282%2Asqrt%28A%29%29%2F%283%5E%281%2F4%29%29