A triangle has sides of 7 cm, 24 cm, and 25 cm. Determine if it is a right triangle, and if so, find the area.
["A triangle has sides of 7 cm, 24 cm, and 25 cm. Determine if it is a right triangle, and if so, find the area.", "Curious about this trio of lengths—7, 24, and 25—curling around a simple question: Is this triangle right-angle? It’s a shape many instantly recognize, but few pause to verify. With trending interest in geometry fundamentals and hands-on DIY projects, understanding triangle types isn’t just for classrooms—it’s practical. This is more than a formula; it’s a foundation that fuels confidence in home improvement, education, and everyday problem-solving across the US.", "### Why A triangle with sides 7 cm, 24 cm, and 25 cm is gaining attention", "The dimensions 7, 24, and 25 form a well-known Pythagorean triple. Though not the most common, this combination stands out for its mathematical clarity and real-world application. Rounded yet precise, these measurements frequently appear in educational content, fitness gear design, and modular furniture planning. Their clarity sparks curiosity—especially in fields like architecture, engineering, and interactive learning apps—where accuracy builds trust. People are increasingly drawn to deconstructing geometric shapes to understand why they behave the way they do, especially with so many DIY and mobile-friendly tools available.", "### How to determine if a triangle is right-angled—and calculate its area", "To verify if a triangle is right-angled, apply the Pythagorean theorem: the square of the longest side (hypotenuse) must exactly equal the sum of the squares of the other two sides. For the triangle with sides 7, 24, and 25, the longest side is 25.", "Check: \n\( 7^2 + 24^2 = 49 + 576 = 625 \) \n\( 25^2 = 625 \)", "Since both values match, this is a right triangle.", "To find the area, use the familiar formula: \nArea = \( \frac{1}{2} \ imes \ ext{base} \ imes \ ext{height} \) \nUsing 7 cm and 24 cm as perpendicular sides: \nArea = \( \frac{1}{2} \ imes 7 \ imes 24 = 84 \) cm².", "### Common questions people ask", "H3: What counts as a “right triangle”? \nA right triangle has one 90-degree angle, confirmed by satisfying \( a^2 + b^2 = c^2 \) with side c as the longest.", "H3: Why does this shape matter in real life?"]
