A triangle has sides of lengths 7, 24, and 25 units. Is this triangle a right triangle?
["Is a Triangle with Sides 7, 24, and 25 Units a Right Triangle? A Full Geometry Analysis", "When examining a triangle with side lengths 7, 24, and 25 units, one key question immediately arises: Is this triangle a right triangle? At first glance, the numbers may look unusual, but by applying fundamental geometric principles—specifically the Pythagorean Theorem—we can confidently determine whether this triangle fits the definition of a right-angled triangle.", "## What Defines a Right Triangle?", "A triangle is classified as a right triangle if one of its angles measures exactly 90 degrees. According to the Pythagorean Theorem, this condition is satisfied when the square of the longest side (called the hypotenuse) equals the sum of the squares of the other two sides. In mathematical terms:", "[\na^2 + b^2 = c^2\n]", "where ( c ) is the longest side (hypotenuse), and ( a ) and ( b ) are the other two sides.", "## Analyzing the Triangle Sides: 7, 24, 25", "The triangle in question has sides measuring:", "- ( a = 7 ) units\n- ( b = 24 ) units\n- ( c = 25 ) units", "Since ( 25 ) is clearly the longest side, it serves as the potential hypotenuse. We apply the Pythagorean Theorem:", "[\n7^2 + 24^2 = 49 + 576 = 625\n]", "Now calculate the square of the hypotenuse:", "[\n25^2 = 625\n]", "## Comparison and Conclusion", "Comparing both results:", "[\n7^2 + 24^2 = 625 = 25^2\n]", "The equation holds true. Therefore, triangle with sides 7, 24, and 25 units is indeed a right triangle, with the right angle opposite the side of length 25 units.", "This special triple — 7, 24, 25 — is a well-known Pythagorean triple, meaning it appears frequently in geometry problems due to its whole-number solutions satisfying the Pythagorean Theorem. Recognizing such triangles helps students, teachers, and enthusiasts quickly identify right triangles without needing to measure angles.", "In summary: The triangle with side lengths 7, 24, and 25 units satisfies the Pythagorean condition and is therefore a classic example of a right triangle. Whether studying geometry, preparing for exams, or exploring mathematical patterns, this triangle stands out as a reliable and teachable case of right-angled geometry.", "---", "Keywords: right triangle, Pythagorean theorem, triangle with sides 7, 24, 25, right triangle verification, geometry, 7-24-25 triangle, acute, obtuse, right triangle exemple", "Meta Description:\nDiscover if a triangle with sides 7, 24, and 25 units is a right triangle. Learn how to use the Pythagorean Theorem to identify right triangles and explore the properties of this well-known Pythagorean triple."]
