Problem 17 · 2016 Math Kangaroo
Medium
Spatial & Visual Reasoning
paper-cuttingfolding
A 3 cm wide strip of paper is dark on one side and light on the other. The folded strip lies exactly inside a rectangle 27 cm long and 9 cm wide (see diagram). How long is the strip of paper?
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Answer: D — 57 cm
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Hint 1 of 3
The strip is 3 cm wide and fills a 27 cm by 9 cm rectangle, which is three strip-widths tall.
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Hint 2 of 3
Unroll the zig-zag: each slanted fold spans the full 9 cm height, so it is longer than a flat 3 cm-wide piece would be.
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Hint 3 of 3
Add the flat horizontal runs to the longer slanted fold pieces.
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Approach: unroll the folded strip and add the pieces
- The 3 cm wide strip lies inside the 27 by 9 rectangle (three strip-widths tall), folding up and down as a zig-zag.
- Unrolling it, the flat horizontal stretches plus the slanted fold pieces (each crossing the full 9 cm height) recombine into one straight strip.
- Summing the straight runs and the longer slanted pieces gives a total length of 57 cm.
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