A triangle has sides of lengths 7, 24, and 25. Determine if it is a right triangle and calculate its area.
["A triangle has sides of lengths \n7, 24, and 25. \nDetermine if it is a right triangle and calculate its area.", "This simple yet powerful set of side lengths is sparking curiosity across digital platforms, including responsible Discover searches, where users seek clear answers backed by facts. The 7-24-25 triangle stands out as a classic example tied to geometry fundamentals—and with good reason.", "### Why A triangle has sides of lengths 7, 24, and 25 is gaining attention in the US", "In recent months, geometric shapes—especially right triangles—have seen renewed interest driven by both educational trends and real-world applications. The 7-24-25 triangle frequently appears in curricula, home projects, and digital learning content because it perfectly aligns with the Pythagorean Theorem: \(7^2 + 24^2 = 49 + 576 = 625 = 25^2\). This relationship makes it a go-to example for teaching right triangles in everyday life.", "Beyond classrooms, the triangle’s structure resonates in fields like architecture, design, and engineering, where efficient layouts and spatial calculations matter—among rising trends in sustainable building and smart space planning. Americans are increasingly drawn to practical math for personal and professional use, fueling demand for clear, accessible explanations like ours.", "### How A triangle has sides of lengths 7, 24, and 25 actually forms a right triangle", "Using the Pythagorean Theorem, a triangle is right-angled when the sum of the squares of the two shorter sides equals the square of the longest side, also known as the hypotenuse.", "- \(7^2 = 49\) \n- \(24^2 = 576\) \n- \(25^2 = 625\)", "Adding the squares of 7 and 24: \n\(49 + 576 = 625\) — exactly matching \(25^2\).", "This confirms that the triangle with sides 7, 24, and 25 satisfies the geometric condition for a right-angle triangle, making it one of the most commonly referenced Pythagorean triples in American education and professional reference.", "### Calculating the area of the triangle", "Once confirmed as a right triangle, calculating area is straightforward. Right triangles offer a clear baseline: legs as the base and height.", "Area = \(\frac{1}{2} \ imes \ ext{base} \ imes \ ext{height}\) \nHere, the legs are 7 and 24.", "Area = \(\frac{"]
