To find the measure of the other leg in a right triangle, we can use the Pythagorean theorem, which states:
\[ a^2 + b^2 = c^2 \]
where:
- \(a\) and \(b\) are the lengths of the legs of the triangle,
- \(c\) is the length of the hypotenuse.
In this case, we know:
- One leg \(a = 16 , \text{cm}\)
- The hypotenuse \(c = 20 , \text{cm}\)
We need to find the other leg \(b\). Plugging the known values into the Pythagorean theorem gives us:
\[ 16^2 + b^2 = 20^2 \]
Calculating the squares:
\[ 256 + b^2 = 400 \]
Now, subtract \(256\) from both sides to isolate \(b^2\):
\[ b^2 = 400 - 256 \] \[ b^2 = 144 \]
Now, take the square root of both sides to find \(b\):
\[ b = \sqrt{144} = 12 , \text{cm} \]
Thus, the measure of the other leg is:
\[ \boxed{12} , \text{cm} \]