A right triangle has legs of length 9 cm and 12 cm. Find the length of the hypotenuse.

Use the Pythagorean theorem:
a^2 + b^2 = c^2

Here, the legs are 9 cm and 12 cm, and c is the hypotenuse.

Substitute the known values:
9^2 + 12^2 = c^2

Simplify:
81 + 144 = c^2
225 = c^2

Take the positive square root of both sides:
c = 15

Therefore, the hypotenuse is 15 cm.