Problem 19 · 2015 Math Kangaroo
Medium
Algebra & Patterns
substitutionperimeter
Eva added the lengths of three sides of a rectangle and obtained 44 cm. Ulli also added the lengths of three sides of the same rectangle and obtained 40 cm. What is the perimeter of the rectangle?
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Answer: B — 56 cm
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Hint 1 of 2
Each person added three sides, so together their sums use the sides a known number of times.
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Hint 2 of 2
Adding the two results counts the length three times and the width three times: 3 times (length + width).
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Approach: add the two three-side sums
- One person summed two lengths and a width, the other two widths and a length.
- Adding their results, 44 + 40 = 84, counts three lengths and three widths: 3(L + W) = 84.
- So L + W = 28 and the perimeter is 2(L + W) = 56.
- The perimeter is 56 cm (B).
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