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 This brainteaser was supplied by the Mathematical Olympiads for Elementary and Middle Schools (www.moems.org). The length and width of a rectangle are whole numbers of centimeters. Neither is divisible by 6. The area of the rectangle is 36 square centimeters. What is the perimeter of the rectangle, in centimeters? Resources for Teaching Math
© 2009 National Council of Teachers of Mathematics, Inc.
http://illuminations.nctm.org
Solution: 26 centimeters. If the area is 36 square centimeters and the length and width are whole numbers, the only possibilities are 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6. The only pair in which neither number is divisible by 6 is 4 × 9, in which case the perimeter is 2(4 + 9) = 26 centimeters. Resources for Teaching Math
© 2009 National Council of Teachers of Mathematics, Inc.
http://illuminations.nctm.org
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