A triangle has sides of lengths 7, 24, and 25. Is this a right triangle? If so, identify the hypotenuse.
["### Is a Triangle with Sides 7, 24, and 25 a Right Triangle?", "When studying triangles in geometry, one of the most fundamental questions is whether a triangle is a right triangle—a shape where one angle measures exactly 90 degrees. A key method to determine this is by applying the Pythagorean Theorem, which states that for a right triangle:", "[\na^2 + b^2 = c^2\n]", "where ( c ) is the longest side (the hypotenuse), and ( a ) and ( b ) are the other two sides.", "Let’s examine the triangle with sides measuring 7, 24, and 25.", "#### Step 1: Identify the longest side\nThe longest side is 25, so if this is a right triangle, 25 must be the hypotenuse.", "#### Step 2: Apply the Pythagorean Theorem\nCalculate:\n[\n7^2 + 24^2 = 49 + 576 = 625\n]\n[\n25^2 = 625\n]", "Since both sides of the equation are equal (( 625 = 625 )), the triangle satisfies the Pythagorean condition.", "#### Conclusion:\nYes, this triangle is a right triangle, and 25 is the hypotenuse—the side opposite the right angle and the longest side.", "This makes the triangle a primitive Pythagorean triple—one of the classic sets of whole numbers used in geometry: ( (7, 24, 25) ). Recognizing such triples helps students and learners quickly identify right triangles without checking angles definitively.", "#### Why This Matters\nUnderstanding whether a triangle is right-angled simplifies solving problems involving area, trigonometry, and coordinate geometry. Knowing 7-24-25 as a Pythagorean triple also helps in timed tests, math exams, and real-world applications like construction and design.", "---", "Keywords: Pythagorean theorem, right triangle 7 24 25, hypotenuse identification, geometric properties, triangle right angle determination, 7-24-25 triangle, geometric proofs, math education.", "Meta Description:\nIs a triangle with sides 7, 24, and 25 a right triangle? Learn how to verify it using the Pythagorean Theorem and discover that 25 is the hypotenuse. Clear, detailed explanation with real-world geometry applications."]
