A right triangle has legs of lengths 9 cm and 12 cm. calculate the length of the hypotenuse?

Let the legs of the triangle be a and b, and the hypotenuse c.

Your first instinct might tell you to use the Pythagorean theorem to go about solving this because [tex]c= \sqrt{a^{2}+b^{2}} [/tex]. This works, but it is slow.

The fastest way to solve this is to recognize that the right triangle is a special triangle where the ratio of the sides are 3:4:5. This means that if the legs are 9 and 12, then the hypotenuse is 15 because 3*3 is 9, 3*4 is 12, and 3*5 is 15.