A triangle has sides of lengths 7 cm, 10 cm, and 5 cm. Is it a valid triangle?

Fri, 08 May 2026 22:59:37 +0000

**A triangle has sides of lengths 7 cm, 10 cm, and 5 cm. Is it a valid triangle?**
When examining whether a set of lengths can form a triangle—like 7 cm, 10 cm, and 5 cm—users often wonder if the shape is physically possible. This simple query reflects a growing curiosity about geometry, proportions, and design across many areas of everyday life, from DIY projects to digital visuals. Understanding why these measurements work (or don’t) offers insight into both basic math and real-world planning. Alright, do these dimensions actually make a triangle? The short answer is: yes, a triangle with sides measuring 7 cm, 10 cm, and 5 cm is geometrically valid. To confirm, we apply a fundamental rule: the triangle inequality theorem. This principle states that for any three lengths to form a triangle, the sum of any two sides must be greater than the third. Let’s test this with the given values:
- 7 + 10 = 17 cm, which is greater than 5 cm
- 10 + 5 = 15 cm, which is greater than 7 cm
- 7 + 5 = 12 cm, which is greater than 10 cm All conditions are satisfied. This confirms a proper triangle is formed—each side is shorter than the sum of the other two, satisfying all requirements. Beyond basic validation, the mix of 5 cm, 7 cm, and 10 cm invites exploration into design and measurement common in kitchen tools, fitness gear, architectural details, and even gaming interfaces. The scale brings familiarity—often recognizable hand spans, tool lengths, or material cuts—while reinforcing foundational geometry concepts. For curious learners in the US seeking clarity, this simple inquiry reflects a broader interest in practical math and spatial reasoning.