But the formula for height in eqilateral triangle is (x(sqrt)/2.
It's not true.
Let's forget about the degrees.
consider all the sides in an equilateral triangle is X.
draw the height for this triangle. One side is now divided into half which each is X/2
as you know in right triangles if hypotenuse is C and two other sides are A and B then the following formula holds.
C^2 = A^2 + B^2
So in the above right triangle we have:
(Height)^2 + (X/2)^2 = X^2
So (Height)^2 = 3(X^2)/4 then we can say that Height is (X/2)*sqrt(3)

For more explanations on degrees, you should know that in Right triangles the side in front of the 30 degree angle is half of the hypotenuse and the side in front of the 60 degree angle is sqrt(3)/2 of the hypotenuse(calculations using sin and cos)
Bests
Arash

The short answer to your question is that in one case, you are calling the side of the equilateral triangle x, but in the other case, you are calling it 2x.

If the equilateral triangle has a side of 2x, the height is x*sqrt(3).
If the equilateral triangle has a side of x, the height is x*sqrt(3)/2.

Along these lines, make sure you take this opportunity to memorize the area of an equilateral triangle with side x: (x^2)*sqrt(3)/4.

More on this here: https://blog.gmatboost.com/2011/08/02/me ... -triangle/

Thank you gmatboost! That definitely explains my false reasoning! How could I not see that before....

Thanks a lot!