Problem 10 · 2013 Math Kangaroo
Medium
Geometry & Measurement
perimeter
Maria drew the figures below on square sheets of paper (each shape is shaded on its own square sheet). How many of these figures have the same perimeter as the square sheet of paper itself?
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Answer: C — 4
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Hint 1 of 3
The plain square sheet has a border equal to its 4 sides.
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Hint 2 of 3
Trace each shape's edge and watch what a notch does: a step in must be matched by a step back out.
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Hint 3 of 3
A bump or dent that goes in and comes straight back keeps the border length the same.
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Approach: compare each outline's perimeter to the square
- Trace the border of each figure and compare it to the square's 4-side border.
- Most of the cut shapes have notches where every step inward is balanced by an equal step outward, so their border stays the same as the square's; one shape gains extra edge.
- Counting the matching ones gives 4 figures, which is choice C.
Mark:
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