Geometry

[tdkk123]

Need a detailed solution for the below problem

What is the side of the square of the largest size that can be symmetrically inscribed in
an equilateral triangle of side 12?

OA [spoiler]12√3 / (2 + √3)[/spoiler]

[cans]

what do you mean by symmetrically inscribed?
Because if a square is inscribed i think it means that all the four corners lie on triangle. and there are only 3 sides.

[tdkk123]

I guess it would look something like this

[cans]

but that's not symmetrical.
(Y and Z have different view)

[cans]

I guess it would look something like this

If you take this figure,
let side of square=x. then 12 = x + 2XA (XA=DZ)
also tan 60 = x/XA -> XA = x/root(3)
12 = x + 2x/(root(3))
x = [12*root(3)] / (2 + root(3))

[GMATGuruNY]

Need a detailed solution for the below problem

What is the side of the square of the largest size that can be symmetrically inscribed in
an equilateral triangle of side 12?

OA [spoiler]12√3 / (2 + √3)[/spoiler]

Since the sides of the square in the figure above must be equal:
x√3 = 12-2x
2x + x√3 = 12
(2+√3)x = 12
x = 12/(2+√3).

Thus, each side of the square = x√3 = 12√3/(2+√3).