Problem 30 · 2023 Math Kangaroo
Stretch
Geometry & Measurement
perimeterarea-decomposition
The diagram shows the map of a big park. The park is split into several sections and the number in each section states its perimeter in km. How big is the perimeter of the entire park in km?
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Answer: C — 26
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Hint 1 of 2
The sum of all the section perimeters counts every internal wall twice and the outer boundary once.
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Hint 2 of 2
Outer perimeter = (sum of all section perimeters) − 2×(total internal wall length).
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Approach: the shared interior walls get counted twice
- Add up the perimeter labels of all the sections.
- In that total, every wall on the park's outer edge is counted once, but every wall shared between two sections is counted twice (once by each section).
- So the park's true perimeter equals the sum of all section perimeters minus twice the total length of the interior dividing walls.
- Carrying out that subtraction with the figure's lengths leaves 26 km (choice C).
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