Problem 17 · 2013 Math Kangaroo
Hard
Geometry & Measurement
careful-counting
Tarzan wanted to draw a rhombus made up of two equilateral triangles, but he drew the line segments inaccurately. When Jane checked the four marked angles, she saw that they are not all equal (see diagram). Which of the five line segments in this diagram is the longest?
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Answer: A — AD
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Hint 1 of 2
In any triangle, the longest side lies opposite the largest angle.
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Hint 2 of 2
Compare the marked angles across both triangles to see which single segment is the longest of all five.
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Approach: use longest-side-opposite-largest-angle across the figure
- The figure is two near-equilateral triangles whose marked angles are slightly unequal.
- In each triangle the longest side is opposite its biggest angle; comparing the labelled angles across the whole figure singles out one segment as longest overall.
- That longest segment is AD.
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