Problem 8 · 2020 Math Kangaroo
Medium
Geometry & Measurement
perimeterspatial-reasoning
There are several figures that can be formed by nine squares of 1 cm side placed side by side (an example is shown), and one of them has the biggest perimeter. What is this perimeter?
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Answer: E — 20 cm
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Hint 1 of 2
Every time two squares share an edge, the total perimeter drops by 2.
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Hint 2 of 2
To make the perimeter biggest, join the nine squares with as few shared edges as possible.
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Approach: minimise shared edges to maximise perimeter
- Nine separate squares have 9 × 4 = 36 unit edges.
- Connecting them needs at least 8 shared edges, each removing 2.
- Largest perimeter = 36 − 2×8 = 20 cm (e.g. a straight strip).
- So the biggest perimeter is 20 cm.
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