### Brain Teasers

# Square Peg

They say you can't put a square peg into a round hole, but it really depends on the sizes of the peg and the hole. What is the maximum size of a square peg that can be inserted into a round hole that is two centimeters in diameter?

### Hint

Think Pythagoras!### Answer

The square root of two, or approximately 1.414 centimeters.If the round hole is two cm. in diameter, a square peg that fits exactly inside it would have a diagonal equal to its diameter. A diagonal and two adjacent sides of the peg form an isosceles right triangle with the diagonal forming the hypotenuse. The sum of the squares of each of the two sides equals the square of the diagonal. This boils down to the square root of two, or approximately 1.414 centimeters.

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