Investigating Triangle Formations with Pencils

Dec 09, 2025

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This investigation explores the formation of triangles using three randomly selected pencils of various sizes. The pupil aims to discover how many different triangles can be formed and identifies the right-angled triangles among them. Through careful analysis, it is determined that there are 23 possible triangle combinations, with specific combinations, such as 5, 12, 13 and 8, 15, 17, qualifying as right-angled triangles. This exercise highlights the principles of geometry and the relationship between side lengths in triangle formation.

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Investigating Triangle Formations with Pencils

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Presentation Transcript

Pencil Problem An Investigation
The diagrams show a number of pencils of various sizes.
A pupil picks up three pencils at random and forms a triangle. • How many different triangles can he actually form? • How many of these triangles will be right angled triangles?
Solution 23 possibilities 5,12,13 8,15,17 give the right angled triangles.