Problem 24 · 2018 Math Kangaroo
Stretch
Geometry & Measurement
area
The figure shown consists of one square part and eight rectangular parts. Each part is 8 cm wide. Peter rearranges all the parts to form one long rectangle that is 8 cm wide. How long is this rectangle?
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Answer: D — 200 cm
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Hint 1 of 2
Every piece is 8 cm wide, so when laid end to end the new rectangle stays 8 cm wide; only total area matters.
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Hint 2 of 2
Find the total area of the original figure, then divide by 8 to get the length.
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Approach: conserve area: length = total area / width
- All nine parts have width 8 cm, so reassembling them into one 8 cm-wide rectangle keeps the same total area.
- The original figure is a square whose area equals the sum of all the parts.
- Dividing that total area by the 8 cm width gives a length of 200 cm.
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