The hypotenuse of a right triangle is 20 centimeters, and the shorter leg is 12 centimeters. find the length of the other leg.

The relationship of the sides of a right triangle is described as
a^2 + b^2 = c^2
where c is the hypotenuse and the legs are a and b

in this case
c = 20
and
b = 12

we plug this into the equation and get
a^2 + 12^2 = 20^2

this simplifies to
a^2 + 144 = 400

we can subtract 144 from both sides
a^2 = 256

then square root both sides
so
a = 16

therefore the length of the other leg is  16 centimeters