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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Comments
I love math riddles and wish there were more. Very well done
I thought, you meant the AREA, which is 2 square cm.
You have a good point there, kwelchans; I probably should have said, "what is the maximum side of a square peg...?"
And you are right; the area would be two centimeters squared.
And you are right; the area would be two centimeters squared.
BTW good teaser
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