What is the length of the hypotenuse of a right triangle where the two sides are 9 units and 12 units long?

Answer 1

The length of the hypotenuse will be 15 units. The rule is that the sum of the squares of the two sides will equal the square of the hypotenuse. The sides are 9 and 12, and the squares are 81 and 144 respectively. They sum to 225, and that's the square of the hypotenuse. The square root of 225 is 15, and that's the number of units that is the length of the hypotenuse. There are some right triangles that have all sides with lengths in integers (counting numbers or "whole" numbers). They include a 3, 4, 5 triangle, a 5, 12, 13 triangle, and a few others. The thing is, any time you have a right triangle like one of these, a multipleof the lengths will also be a valid right triangle. For the 3, 4, 5 triangle, if you multiply each side by 2, you'll get a 6, 8, 10 triangle. This "new" triangle will obey the Pythagorean theorem. In the 3, 4, 5 triangle, 32 = 9, 42 = 16 and 52 = 25; and 9 + 16 = 25 so it checks. Same with a 6, 8, 10 triangle. In that one, 62 = 36, 82 = 64 and 102 = 100; and 36 + 64 = 100, so that checks as well. Why'd we go through that? Check this out. If we take a 3, 4, 5 triangle and multiply all sides by 3, we'll get a 9, 12, 15 triangle. Do those numbers look familiar? They are eerily similar to the ones in the question.