Problem 13 · 2017 Math Kangaroo
Medium
Geometry & Measurement
ratio
The black line and the dashed line together form seven equilateral triangles. The dashed line is 20 cm long. How long is the black line?
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Answer: D — 40 cm
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Hint 1 of 2
In each small equilateral triangle, compare how much of the outline is dashed versus black.
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Hint 2 of 2
Across all seven triangles the black total is a fixed multiple of the dashed total.
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Approach: ratio of black to dashed side-lengths
- The dashed line forms the bases of the equilateral triangles; the black line forms their slanted sides.
- Counting segments, the black length comes out as twice the dashed length.
- So the black line is 2 × 20 = 40 cm.
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