Problem 16 · 2011 Math Kangaroo
Hard
Geometry & Measurement
perimeterarea
A square piece of paper is cut into six rectangular pieces as shown. The sum of the perimeters of the six pieces is 120 cm. How big is the area of the square?
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Answer: D — 144 cm²
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Hint 1 of 2
The six perimeters together include the outside edges plus the internal cut lines counted twice.
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Hint 2 of 2
Express that total in terms of the side length s, set it to 120, and solve.
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Approach: relate the total of the six perimeters to the square's side
- When the square (side s) is cut into the six rectangles shown, the cut segments add length.
- Adding up all six perimeters counts the square's outer edge plus twice every internal cut.
- For this cut pattern that total equals 120 cm exactly when s = 12, so the area is 12² = 144 cm².
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