Problem 13 · 2013 Math Kangaroo
Medium
Geometry & Measurement
Number Theory
casework
The perimeter of a trapezium is 5, and all of its side lengths are whole numbers. How big are its two smallest angles?
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Answer: B — 60° and 60°
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Hint 1 of 2
Whole-number sides adding to 5 leave very few shapes — list them.
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Hint 2 of 2
A trapezium with sides 2,1,1,1 is half of an equilateral triangle's partner; find its base angles.
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Approach: enumerate integer sides, then read the angles
- Four whole-number sides summing to 5 must be 2, 1, 1, 1.
- These form an isosceles trapezium with parallel sides 2 and 1 and slant sides 1.
- That trapezium is three equilateral triangles joined, so its smallest (base) angles are 60° each.
- The two smallest angles are 60° and 60°.
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