First, find hypotenuse: \( \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \) cm.
["# How to Find the Hypotenuse: A Simple Guide Using the Pythagorean Theorem", "When solving right triangle problems, one of the most essential skills is calculating the hypotenuse. Whether you're a student learning geometry or someone tackling practical measurements, understanding how to find the hypotenuse using the Pythagorean Theorem is invaluable. In this article, we'll walk through the step-by-step process with a clear example: how to find the hypotenuse when given two leg lengths.", "## What Is the Hypotenuse?", "In a right triangle, the hypotenuse is the side opposite the right angle. It’s the longest side and plays a crucial role in the Pythagorean Theorem:", "[\nc = \sqrt{a^2 + b^2}\n]", "where:\n- ( c ) is the hypotenuse\n- ( a ) and ( b ) are the lengths of the other two legs", "## Step-by-Step: Finding the Hypotenuse", "Let’s apply the formula using a classic example: finding the hypotenuse when the legs measure 9 cm and 12 cm.", "### Step 1: Write down the formula\nStart with the Pythagorean Theorem:\n[\nc = \sqrt{a^2 + b^2}\n]", "### Step 2: Plug in the values\nHere, ( a = 9 ) cm and ( b = 12 ) cm:\n[\nc = \sqrt{9^2 + 12^2}\n]", "### Step 3: Calculate the squares\nSquare each leg:\n[\n9^2 = 81\n\quad \ ext{and} \quad\n12^2 = 144\n]", "### Step 4: Add the squared values\n[\n81 + 144 = 225\n]", "### Step 5: Take the square root\n[\nc = \sqrt{225} = 15\n]", "### Final Result:\nThe hypotenuse measures 15 cm.", "---", "## Why This Matters", "Knowing how to calculate the hypotenuse is essential not only in classroom math but also in real-world scenarios such as construction, navigation, and engineering. Whether you’re measuring a diagonal, calculating diagonal distances on a screen, or designing structures, mastering this fundamental principle helps build confidence in solving geometric problems.", "## Pro Tip: Quick Visual Check", "Remember, the hypotenuse sits across from the right angle and forms a “perfect square” rectangle when squared. If ( a^2 + b^2 = c^2 ), you’re on the right track—just be sure to take the square root at the end!", "---", "By following this simple formula and practicing with different values, you’ll master finding the hypotenuse and strengthen your geometry skills step by step.", "Keywords: hypotenuse calculation, Pythagorean Theorem, how to find hypotenuse, right triangle formula, calculate hypotenuse, square root in geometry, geometry tutorial, math help hypotenuse, find hypotenuse 9 and 12, 15 cm hypotenuse example."]
