A triangle has sides of length 7 cm, 10 cm, and 5 cm. Is it a valid triangle? Justify your answer using the triangle inequality theorem.

Thu, 07 May 2026 00:02:22 +0000

# Is a Triangle with Sides 7 cm, 10 cm, and 5 cm Valid? Understanding the Triangle Inequality Theorem A triangle with sides 7 cm, 10 cm, and 5 cm sparks quiet curiosity—why is that? In today’s digital space, questions like this often circulate alongside broader interest in geometry, design, and construction. At first glance, the numbers seem simple, but validating a triangle’s structure hinges on a foundational mathematical principle: the triangle inequality theorem. This well-established rule shapes how we understand shape formation—and why not all combinations form a closed triangle. The triangle inequality theorem states that for any three lengths to form a valid triangle, the sum of any two side lengths must always be greater than the third side. This principle isn’t just academic—it ensures structural stability in real-world applications, from architecture to manufacturing. Understanding why these specific sides work (or don’t) connects to bigger trends in STEM education and practical problem-solving in US homes, schools, and workplaces. ## The Numbers: 7, 10, and 5—Can They Form a Triangle?