A triangle has sides of lengths 7, 24, and 25. Determine if it is a right triangle.
["Is Triangle With Sides 7, 24, and 25 a Right Triangle? A Mathematical Analysis", "When studying triangles, one of the most common and important questions is whether a given set of side lengths forms a right triangle. In this article, we examine a triangle with sides measuring 7, 24, and 25 to determine if it satisfies the conditions of a right triangle.", "A triangle is classified as a right triangle if one of its angles measures exactly 90 degrees. The primary mathematical tool used to verify this property is the Pythagorean Theorem, which states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.", "### Applying the Pythagorean Theorem to Sides 7, 24, and 25", "Let the triangle have sides (a = 7), (b = 24), and (c = 25), where (c) is the longest side. According to the Pythagorean Theorem:", "[\na^2 + b^2 = c^2\n]", "Calculating both sides:", "[\n7^2 + 24^2 = 49 + 576 = 625\n]", "[\n25^2 = 625\n]", "Since both sides of the equation are equal ((625 = 625)), the triangle satisfies the Pythagorean condition.", "### Conclusion: It Is a Right Triangle", "Yes, a triangle with sides 7, 24, and 25 is a right triangle, with side 25 being the hypotenuse. This confirms not only its geometric validity but also its place among Pythagorean triples—sets of three positive integers that form the sides of a right triangle.", "This particular triple is one of the most well-known:\n[\n(7, 24, 25)\n]\nIt appears frequently in geometry education and real-world applications like construction, architecture, and physics, where quick verification of right angles is essential.", "Understanding triangle classifications like this strengthens spatial reasoning and supports deeper comprehension of trigonometric principles and coordinate geometry.", "---", "Keywords: right triangle, Pythagorean theorem, triangle sides 7 24 25, check if triangle is right, 7-24-25 triangle, mathematical verification, geometry, right triangle definition", "Meta Description:\nIs a triangle with sides 7, 24, and 25 a right triangle? This article confirms it is, using the Pythagorean Theorem and provides a clear explanation with calculations. Ideal for math students and educators.", "---", "Additional Tips:\nIf you're ever asked whether a triangle is right-angled, quickly square the side lengths and check if (a^2 + b^2 = c^2). This method is fast and reliable."]
