Question

An old adage states that "You can't fit a square peg in a round hole." Actually, you can, it just won't fill the hole. If a hole is 4 inches in diameter, what is the approximate width of the largest square peg that fits in the round hole?

Answer 1

Suppose the peg is like a rectangular prism:

It will be a right triangle with two sides of 2 and 2 because the diameter is 4.
c=√(2²+2²)
c=2√2
so the width of the largest peg is 2√2 or 2.83 inch