Question:** In a right triangle, the lengths of the legs are 7 units and 24 units. What is the length of the hypotenuse?
["Question: In a Right Triangle with Legs of 7 Units and 24 Units, What is the Length of the Hypotenuse?", "When working with right triangles, one of the most fundamental questions students and learners frequently ask is: What is the length of the hypotenuse when the two legs are known? If you have a right triangle where one leg measures 7 units and the other leg measures 24 units, calculating the hypotenuse is quick using the Pythagorean Theorem.", "### What is the Pythagorean Theorem?", "The Pythagorean Theorem states that in any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two legs. Mathematically, it’s expressed as:", "$$\nc^2 = a^2 + b^2\n$$", "Where:\n- $ c $ is the length of the hypotenuse\n- $ a $ and $ b $ are the lengths of the legs", "### Applying the Values", "In your triangle:\n- $ a = 7 $\n- $ b = 24 $", "Plug these values into the theorem:", "$$\nc^2 = 7^2 + 24^2\n$$\n$$\nc^2 = 49 + 576\n$$\n$$\nc^2 = 625\n$$", "Now, take the square root of 625 to find $ c $:", "$$\nc = \sqrt{625} = 25\n$$", "### Answer: The Length of the Hypotenuse is 25 Units", "So, in a right triangle with legs measuring 7 units and 24 units, the hypotenuse is exactly 25 units long. This classic example appears often in geometry and algebra, serving as a key example of how the Pythagorean Theorem applies in real right triangles.", "### Why This Matters", "Understanding how to find the hypotenuse using the Pythagorean Theorem is essential not only for basic geometry but also in fields like architecture, physics, engineering, and navigation. Whether you're measuring distances, designing structures, or solving applied problems, this foundational concept remains indispensable.", "---", "Keywords for SEO:\nright triangle hypotenuse, Pythagorean Theorem example, calculate hypotenuse, legs 7 and 24 units, right triangle right angle triangle solution, math problem help, geometry formula, how to find hypotenuse, triangle side length calculation", "Meta Description:\nLearn how to find the hypotenuse of a right triangle with legs measuring 7 units and 24 units using the Pythagorean Theorem. Step-by-step solution and explanation.", "---", "Use this guide every time you need a fast, accurate way to determine the hypotenuse—because in a right triangle with legs 7 and 24, the hypotenuse is always 25 units."]
