Problem 3 · 2021 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracing
A park is shaped like an equilateral triangle. A cat wants to walk along one of the three indicated paths (thicker lines) from the upper corner to the lower-right corner. The lengths of the paths are P, Q and R, as shown. Which statement about the lengths of the paths is true?
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Answer: B — \(P
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Hint 1 of 2
Every path starts at the top corner and ends at the lower-right corner, so they all cover the same overall drop and shift.
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Hint 2 of 2
Replacing a straight horizontal cut with travel along the slanted edge adds length, so compare how much of each path hugs the slant.
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Approach: compare the three traced paths segment by segment
- All three paths join the same two corners, so they share the same net horizontal and vertical change.
- Path P takes the most direct mix of horizontal cuts and short drops, so it is the shortest.
- Path Q runs the most along the slanted edge, where covering the same height costs extra length, so it is the longest, with R in between.
- Therefore \(P
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