Problem 23 · 2012 Math Kangaroo
Stretch
Geometry & Measurement
area-decomposition
A rectangular piece of paper is 60 mm long and 36 mm wide. After making a straight cut you have a square and a leftover piece. You do the same with the leftover piece, and so on, until the leftover piece itself is a square. What is the side length of the last square?
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Answer: E — 12 mm
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Hint 1 of 2
Each cut slices off the biggest square that fits, leaving a smaller rectangle.
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Hint 2 of 2
Repeat the cutting on 60 by 36 and watch the leftover shrink to a square.
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Approach: repeatedly cut off the largest square
- From 60 by 36, cut a 36 by 36 square, leaving 24 by 36.
- From 24 by 36, cut a 24 by 24 square, leaving 24 by 12.
- From 24 by 12, two 12 by 12 squares finish it, so the last square has side 12.
- The last square is 12 mm on a side.
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