A right triangle has legs of lengths 9 and 12. What is the length of the hypotenuse?
["A Right Triangle with Legs 9 and 12: How to Find the Hypotenuse", "When studying right triangles, one of the most essential concepts is the Pythagorean Theorem — a fundamental rule in geometry that helps calculate the length of the hypotenuse. If you’ve come across a right triangle with leg lengths of 9 and 12, you may be wondering: What is the length of the hypotenuse? This article walks you through how to solve this classic problem step by step.", "### Understanding the Pythagorean Theorem", "For any right triangle, the relationship between the legs and the hypotenuse is given by:\n[ c^2 = a^2 + b^2 ]\nwhere:\n- ( c ) is the hypotenuse (the longest side opposite the right angle),\n- ( a ) and ( b ) are the lengths of the two legs.", "---", "### Step-by-Step Calculation", "Given:\n- ( a = 9 )\n- ( b = 12 )", "Substitute the values into the formula:\n[ c^2 = 9^2 + 12^2 ]\n[ c^2 = 81 + 144 ]\n[ c^2 = 225 ]", "Now, take the square root of both sides to solve for ( c ):\n[ c = \sqrt{225} ]\n[ c = 15 ]", "---", "### Final Answer", "The length of the hypotenuse of a right triangle with legs measuring 9 and 12 is 15 units.", "---", "### Why This Matters", "This principle isn’t just theoretical — it applies to architecture, engineering, navigation, and many real-world situations where angles and distances matter. Knowing how to calculate the hypotenuse using the Pythagorean Theorem equips you with a powerful mathematical tool.", "If you’re learning geometry or preparing for exams, practice problems like this one help reinforce your understanding. Remember:\n- Pythagoras’ Theorem works only in right triangles.\n- Squaring the sides prevents errors when summing and taking square roots.", "Keep practicing — solving triangle problems builds confidence and sharpens logical thinking!", "---", "Keywords: right triangle, hypotenuse calculation, Pythagorean Theorem, how to find hypotenuse, leg lengths 9 and 12, geometry formula, right triangle triangle problems."]
