Problem 16 · 2015 Math Kangaroo
Stretch
Geometry & Measurement
factor-pairsperimeter
A rectangle has area 12 cm2. The lengths of the sides are natural numbers. Which perimeter could the rectangle have?
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Answer: B — 26 cm
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Hint 1 of 2
List the whole-number side pairs whose product is 12.
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Hint 2 of 2
Each pair gives a perimeter of 2 × (length + width); see which listed answer can appear.
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Approach: list factor pairs of 12 and compute each perimeter
- Whole-number sides multiplying to 12 are 1×12, 2×6, and 3×4.
- Their perimeters are 2(1+12) = 26, 2(2+6) = 16, and 2(3+4) = 14.
- Among the choices only 26 cm appears, so that is the possible perimeter.
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