Question

In a square with side length of 6, what is the distance between the center of the square and the center of the largest equilateral triangle inscribed inside the square?

Answer 1

Place the right angle at the origin. Short leg on x-axis.
The forth corner of the square is the point on the hypotenuse where the line y = x intersects. (Draw a diagram!)
In this case the hypotenuse is y = -4x/3 + 8
x = -4x/3 + 8
7x/3 = 8
7x = 24
x = 3.428571429