Question

A round hole has a diameter of 2 inches. You have a square peg with sides of 1-1/2 inches. Will the square peg fit into the round hole? Explain please

Answer 1

In order for a square to fit in a circle, the diagonal of the square
can't be greater than the diameter of the circle.

The diagonal of any square is (length of side) times √2 .
The diagonal of THIS square is (1.5) x (√2) = 2.12 inches.
The diameter of the hole is 2 inches.
The peg will not fit into it.