Enigma 480: An irrational question
24 December 2018
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From New Scientist #1631, 22nd September 1988 [link]
Kugelbaum was running through a geometrical proof with some of his students when he suddenly went off at a tangent.
“What an extraordinary rectangle I have just drawn!” he remarked out loud. “Why, the number of inches in the perimeter is an integer equal to the number of square inches in its area. And yet, no one of its sides is a rational number of inches long”. (A rational number is one which can be expressed as the ration of two definite integers: for example 1.5, but not √2).
What is the smallest possible perimeter of such a rectangle, measured in inches?
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