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Problem 36

Geometry Difficulty 1.1 Multiple choice CEMC Gauss (Grade 8) · Canada · 2026

A triangle has side lengths $3~\text{cm}$ , $5~\text{cm}$ , and $x~\text{cm}$ , as shown.

If the perimeter of the triangle is $12~\text{cm}$ , the value of $x$ is

Pick one

Official solution

The perimeter is $12 $\text{}$
cm} $. Thus,$ 3 $\text{}$ cm} + 5 $\text{}$
cm} + x $\text{}$ cm}=12 $\text{}$ cm} $, and so$ x=12-8=4$.

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