A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle?
["# Is a Triangle with Sides 7 cm, 24 cm, and 25 cm a Right Triangle?", "If you’ve ever wondered whether a triangle with side lengths of 7 cm, 24 cm, and 25 cm is a right triangle, you’re not alone! This is a classic geometry question that sparks interest due to the famous Pythagorean triplet connection. In this article, we’ll explore whether this triangle follows the Pythagorean theorem and confirm its classification as a right triangle—complete with the math, real-world examples, and tips for verification.", "## Understanding Right Triangles and the Pythagorean Theorem", "A right triangle is defined as a triangle that contains one 90-degree angle. The foundational rule for identifying right triangles is the Pythagorean theorem, which states:", "> In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.", "Mathematically, this is expressed as:", "[ a^2 + b^2 = c^2 ]", "where ( c ) is the hypotenuse, and ( a ) and ( b ) are the other two legs.", "## The Triangle with Sides 7 cm, 24 cm, and 25 cm", "Given a triangle with sides:", "- Side A = 7 cm\n- Side B = 24 cm\n- Side C = 25 cm (supposedly the longest side, so the potential hypotenuse)", "To determine if it is a right triangle, we test the Pythagorean equation using the two shorter sides as legs and the longest as the hypotenuse:", "[\na^2 + b^2 = c^2 \\n7^2 + 24^2 = 25^2 \\n49 + 576 = 625 \\n625 = 625\n]", "The equation holds true. This confirms that the triangle with sides 7 cm, 24 cm, and 25 cm is indeed a right triangle, with the 25 cm side as the hypotenuse.", "## Real-Life Applications and Examples", "Triangles like this aren’t just theoretical—they appear in architecture, engineering, and design where stability and angles matter. For instance, roof trusses often use right triangles because their dimensions follow the Pythagorean relationship, ensuring structural symmetry and strength.", "## How to Check If a Triangle Is Right-Angled Mathematically", "Here’s a quick method to verify:", "1. Identify the longest side (potential hypotenuse).\n2. Square each side length.\n3. Add the squares of the two shorter sides.\n4. Compare the sum to the square of the longest side.\n - If equal → right triangle.\n - If less → acute triangle.\n - If greater → obtuse triangle. \nIn our example:", "[\n7^2 + 24^2 = 49 + 576 = 625 = 25^2\n]", "Since ( 7^2 + 24^2 = 25^2 ), the triangle is confirmed right-angled.", "## Final Thoughts", "The triangle with side lengths 7 cm, 24 cm, and 25 cm is unquestionably a right triangle because it satisfies the Pythagorean theorem. This simple yet powerful relationship between the sides allows us to confirm right angles efficiently—central to geometry, mathematics, and practical applications alike.", "Whether you're solving textbook problems or exploring geometry in daily life, recognizing this pattern is a valuable skill that builds confidence in understanding triangle properties.", "---", "Keywords: right triangle 7 cm 24 cm 25 cm, Pythagorean theorem, right triangle verification, 7-24-25 triangle, geometry facts, triangle types, math education, right-angle triangle, acute obtuse triangle comparison.", "Meta Description: Is a triangle with sides 7 cm, 24 cm, and 25 cm a right triangle? Discover why this side lengths combination satisfies the Pythagorean theorem and verify it step by step. Perfect for students and math enthusiasts!"]
