Problem 12 · 2012 Math Kangaroo
Medium
Geometry & Measurement
areasubstitution
Ms. Green plants peas (“Erbsen”) and strawberries (“Erdbeeren”) only in her garden. This year she has changed her pea-bed into a square-shaped bed by increasing one side by 3 m. By doing this her strawberry-bed became 15 m² smaller. What area did the pea-bed have before? (In the picture, “alte Beete” means the old beds and “neue Beete” the new beds.)
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Answer: C — 10 m²
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Hint 1 of 2
Increasing one side by 3 m turned the rectangular pea-bed into a square.
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Hint 2 of 2
The 15 m² taken from the strawberries is the strip that was added — use it to find the square's side.
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Approach: set up the added strip
- Let the square pea-bed have side s; before, the pea-bed was (s−3) by s, since one side grew by 3.
- The added strip has area 3 × s and equals the 15 m² lost by the strawberries, so 3s = 15, giving s = 5.
- The original pea-bed area was (s−3) × s = 2 × 5 = 10 m².
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