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, 2005

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

A Nakamoto triangle is a right-angled triangle with integer side lengths which are in the ratio $3:4:5$ . (For example, a triangle with side lengths $9$ , $12$ and $15$ is a Nakamoto triangle.) If one of the sides of a Nakamoto triangle has length $28$ , what are the lengths of the other two sides?

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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. Solutions are the publisher's, linked not copied.