A right triangle has legs of lengths 9 and 12. Find the length of the hypotenuse.
["Title: Find the Length of the Hypotenuse of a Right Triangle with Legs 9 and 12", "Meta Description:\nDiscover how to calculate the hypotenuse of a right triangle when given leg lengths. Learn the Pythagorean theorem application with a real example: legs of 9 and 12.", "---", "### Introduction", "Understanding right triangles is fundamental in geometry, and one of the most essential calculations is finding the hypotenuse—the longest side opposite the right angle. If you have a right triangle with leg lengths of 9 and 12, how do you find the hypotenuse? This article translates the Pythagorean theorem into a clear, step-by-step solution.", "### What Is a Right Triangle?", "A right triangle is defined by having one angle exactly 90 degrees. The two sides forming this right angle are called the legs, while the side opposite (longest) is the hypotenuse. Knowing how to compute the hypotenuse is crucial for solving countless problems in geometry, construction, physics, and beyond.", "### Recalling the Pythagorean Theorem", "The Pythagorean Theorem provides the key formula for right triangles:", "[\nc^2 = a^2 + b^2\n]", "Where:\n- ( c ) = length of the hypotenuse\n- ( a ) and ( b ) = lengths of the legs", "This simple relationship allows you to compute any missing side when two sides are known.", "### Applying the Theorem: Legs of 9 and 12", "Let:\n- ( a = 9 )\n- ( b = 12 )\n- ( c = ? )", "Plug the values into the Pythagorean formula:", "[\nc^2 = 9^2 + 12^2\n]", "Calculate the squares:", "[\nc^2 = 81 + 144 = 225\n]", "Now take the square root of both sides to solve for ( c ):", "[\nc = \sqrt{225} = 15\n]", "### Final Answer", "The length of the hypotenuse is 15 units. This classic right triangle with legs 9, 12, and hypotenuse 15 is known as a Pythagorean triple and serves as a foundational example in geometry.", "### Why This Matter?", "Knowing how to find hypotenuses helps in real-world applications like:\n- Constructing right angles and structures\n- Calculating distances in navigation\n- Designing ramps, roofs, and stairways\n- Teaching spatial reasoning and theorem-based problem solving", "### Summary", "- Given legs ( a = 9 ) and ( b = 12 ), use Pythagoras:\n [\n c = \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15\n ]\n- The hypotenuse is 15.\n- This proof demonstrates the power and simplicity of the Pythagorean Theorem in solving geometric problems.", "---", "Keywords: right triangle, hypotenuse, Pythagorean theorem, legs 9 and 12, geometry, right triangle calculation, math tutorial, algebra\nTarget Audience: Students, educators, geometry learners, math enthusiasts", "---", "Understanding and applying the Pythagorean Theorem empowers you to confidently solve real-life problems involving right triangles—starting immediately with values like 9 and 12!"]
