In a triangle, the hypotenuse is the longest side when the triangle is a right triangle. In this case, the sides are 12, 16, and 20. The longest side here is 20.
To confirm if this is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
\[ c^2 = a^2 + b^2 \]
Let's check:
- Let \( c = 20 \), \( a = 12 \), and \( b = 16 \).
Calculating:
\[ 20^2 = 12^2 + 16^2 \] \[ 400 = 144 + 256 \] \[ 400 = 400 \]
Since the equation holds true, the triangle is indeed a right triangle.
Therefore, the length of the hypotenuse is 20.