Maths Olympiad Prep

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, 2026

Geometry Difficulty 1.2 Junior Find the answer Canada

If a square's side length is a whole number, measured in
centimetres, which of the following could be the perimeter of the
square?

Pick one

Solution

Suppose that each side of the square has length n cmn~\text{cm}, where nn is a whole number. Then the perimeter
of the square is $4×n cm$.\$4\times n~\text{cm}\$. This means that the perimeter of the square in
centimetres is a multiple of 44. Of
the choices given, only 32 cm32~\text{cm} is a multiple of 44.

(We note that in this case, the square has side length n=8 cmn=8~\text{cm}.)

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.