A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

Use the Pythagorean theorem: a² + b² = c², where c is the hypotenuse. Here 6² + 8² = 36 + 64 = 100, so c = √100 = 10. The 6-8-10 triangle is a multiple of the common 3-4-5 right triangle, so recognizing that pattern gives the answer instantly. Be careful: 100 is c², not c — you must take the square root. The hypotenuse is 10. Memorizing common Pythagorean triples (3-4-5, 5-12-13, 8-15-17) speeds up these geometry problems considerably.