What is the length of the hypotenuse of a right triangle with legs of lengths 9 and 12?

Answer 1

The hypotenuse is 15.
The Pythagorean Theorum states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides; in other words, if c is the length of the hypotenuse, and a and b are the lengths of the other two sides:
a2 + b2 = c2

In this case, a = 9 (a2 = 81) and b = 12 (b2 = 144), and a2 + b2 = 81 + 144 = 225. But we know that this is also equal to c2. If c2 = 225, then c = √225 = 15.

Also, just a little thought reveals that this triangle is a "3-4-5" triangle. For any right triangle with non-hypotenuse sides of length 3 and 4 units, the hypotenuse will be 5 units in length. Because units are arbitrary, this relationship extends to multiple of 3, 4, and 5. 9 and 12 are 3 times 3 and 4. So the hypotenuse is 3 times 5, or 15.