To determine if triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem. The theorem states that in a right triangle with legs \( a \) and \( b \) and hypotenuse \( c \), the following equation holds:
\[ a^2 + b^2 = c^2 \]
Here, we need to identify the longest side, which will be considered as the hypotenuse. In this case, the longest side is 50.
Thus, we will check if:
\[ 40^2 + 32^2 = 50^2 \]
Calculating the squares:
- \( 40^2 = 1600 \)
- \( 32^2 = 1024 \)
- \( 50^2 = 2500 \)
Now, adding the squares of the two shorter sides:
\[ 1600 + 1024 = 2624 \]
Now comparing:
\[ 2624 \neq 2500 \]
Since \( 40^2 + 32^2 \) does not equal \( 50^2 \), triangle DEF is not a right triangle.
Therefore, the answer is 0.