Problem 2 · 2013 Math Kangaroo
Easy
Geometry & Measurement
perimeter
Maria has six equally big square pieces of plain paper. On each piece of paper she draws one of the figures shown below. How many of these figures have the same perimeter as the plain piece of paper itself?
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Answer: C — 4
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Hint 1 of 2
A shaded shape has the same perimeter as the whole square only if every cut is balanced by an equal bit of border added.
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Hint 2 of 2
Cutting a notch out of an edge keeps the perimeter the same; count the figures that do not add extra sticking-out edges.
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Approach: compare each figure's boundary length to the plain square
- The plain square has perimeter equal to four side-lengths.
- A shape keeps that same perimeter when its drawn lines only re-trace existing border length without adding extra exposed edges.
- Checking the six figures, exactly 4 of them match the square's perimeter.
- So the answer is 4.
Mark:
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