Problem 13 · 2015 Math Kangaroo
Stretch
Geometry & Measurement
area-decompositionsubstitution
A rectangle is formed from 4 equally sized smaller rectangles. The shorter side is 10 cm long. How long is the longer side?
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Answer: C — 20 cm
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Hint 1 of 2
Two of the small rectangles stand upright and span the full 10 cm height; the other two lie flat, stacked in the middle.
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Hint 2 of 2
An upright rectangle's long side is 10 cm; a stacked rectangle's short side is half of 10. Use that to find both side lengths of a small rectangle.
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Approach: find the small rectangle's sides, then add up the long side of the big one
- Each small rectangle is the same. The two upright ones have long side equal to the full height, 10 cm; the two stacked in the middle split that height, so each has short side 10 ÷ 2 = 5 cm.
- So a small rectangle is 5 cm by 10 cm.
- Along the long side of the big rectangle: upright (5) + stacked length (10) + upright (5) = 20 cm.
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