A round hole has a diameter of 2 inches. You have a square peg with sides of 1.5 inches. Will the square peg fit into the round hole? Explain.

Question

AL2006 · Answer

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.

AL2006 · Answer

The square peg with a diagonal of approximately 2.12 inches will not fit into the round hole with a diameter of 2 inches since the diagonal is greater than the hole's diameter. Therefore, the peg is too large to fit. No fitting occurs when the diagonal exceeds the hole's measurement. 
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A round hole has a diameter of 2 inches. You have a square peg with sides of 1.5 inches. Will the square peg fit into the round hole? Explain.

Answer (2)

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