Problem 21 · 2016 Math Kangaroo
Stretch
Geometry & Measurement
pythagorean-triple
A creeping plant twists exactly 5 times around a post with circumference 15 cm (as shown in the diagram) and thus reaches a height of 1 m. While the plant grows the height of the plant also grows with constant speed. How long is the creeping plant?
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Answer: C — 1.25 m
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Hint 1 of 2
Unroll one full twist into a flat right triangle.
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Hint 2 of 2
Its base is the post's circumference and its height is the rise per twist.
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Approach: unroll the spiral
- Each of the 5 twists rises 100/5 = 20 cm while going 15 cm around.
- One twist's length is √(152+202) = 25 cm.
- Five twists give 5×25 = 125 cm = 1.25 m.
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