The lengths of the legs of a right triangle are 6 cm and 8 cm. what is the length of the hypotenuse?

You require the Pythagorean Theorem: in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.In this case 6^2 + 8^2 = 36 + 64 = 100 = 10^2
 the hypotenuse is 10.

You can find the missing side of a right triangle by using the Pythagorean Theorem (a² + b² = c²), where c is the hypotenuse. So, just plug the given numbers in and solve for c.

a² + b² = c²   Plug 6 and 8 in for a and b (order doesn't matter)
6² + 8² = c²   Square both numbers
36 + 64 = c²   Add
100 = c²   Take the square root of both sides
10 = c   Switch the sides of the equation to make it easier to read
c = 10

So, the hypotenuse of the triangle is 10 cm.