Problem 8 · 2018 Math Kangaroo
Easy
Geometry & Measurement
perimeterarea-decomposition
A large rectangle is made up of 9 equally big rectangles. The longer side of each small rectangle is 10 cm long. What is the perimeter of the large rectangle?
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Answer: C — 76 cm
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Hint 1 of 2
Let the small rectangle be 10 (long) by w (short), and write the big rectangle's sides using the layout.
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Hint 2 of 2
The middle band of standing rectangles fixes the width; the top and bottom rows fix the short side w.
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Approach: set up the dimensions from the 2+5+2 layout
- Five standing rectangles side by side make the width: 5 short sides. Two lying rectangles also span that width, so 2 · 10 = 5w, giving w = 4 cm.
- The big rectangle is 5w = 20 cm wide and (4 + 10 + 4) = 18 cm tall.
- Its perimeter is 2 · (20 + 18) = 76 cm.
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