A right triangle has legs measuring 9 cm and 12 cm. Find the length of the hypotenuse.
["# How to Find the Hypotenuse of a Right Triangle with Legs Measuring 9 cm and 12 cm", "When working with right triangles, one of the most common calculations is finding the length of the hypotenuse—the longest side, opposite the right angle. If you’re dealing with a right triangle where the legs measure 9 cm and 12 cm, this article guides you step-by-step through using the Pythagorean Theorem to calculate the hypotenuse.", "## What is the Pythagorean Theorem?", "The Pythagorean Theorem states that in any right triangle, the square of the hypotenuse ((c)) is equal to the sum of the squares of the other two legs ((a) and (b)):", "[\nc^2 = a^2 + b^2\n]", "This formula is essential for solving for the hypotenuse when the lengths of the two legs are known, as in the case of a 9 cm and 12 cm right triangle.", "## Applying the Theorem to the Triangle", "Here, the leg lengths are:\n- (a = 9) cm\n- (b = 12) cm", "Plug these values into the Pythagorean formula:", "[\nc^2 = 9^2 + 12^2\n]", "Calculate each square:", "[\n9^2 = 81, \quad 12^2 = 144\n]", "Add them together:", "[\nc^2 = 81 + 144 = 225\n]", "Now, take the square root of 225 to solve for (c):", "[\nc = \sqrt{225} = 15 \ ext{ cm}\n]", "## Result: The Hypotenuse is 15 cm", "Thus, the length of the hypotenuse in a right triangle with legs measuring 9 cm and 12 cm is 15 centimeters.", "## Why This Matters in Real Life", "Understanding how to calculate the hypotenuse using the Pythagorean Theorem applies to many practical situations—whether designing structures, calculating distances in surveying, or solving geometry problems in school and professional fields.", "### Final Takeaway", "To quickly recall the hypotenuse of a right triangle with legs 9 cm and 12 cm:", "[\nc = 15 \ ext{ cm}\n]", "This simple yet powerful calculation ensures accurate results in both academic and real-world applications.", "---", "Keywords: right triangle, hypotenuse, Pythagorean Theorem, 9 cm leg, 12 cm leg, math problem, geometry, triangle calculation"]
