To determine if triangle DEF with sides measuring 50, 40, and 32 is a right triangle, we can use the Pythagorean theorem. A triangle is a right triangle if the square of the length of the longest side equals the sum of the squares of the other two sides.
The sides in ascending order are: 32, 40, and 50. The longest side is 50.
Now, we check the Pythagorean theorem:
\[ 50^2 = 40^2 + 32^2 \]
Calculating each side:
\[ 50^2 = 2500 \] \[ 40^2 = 1600 \] \[ 32^2 = 1024 \]
Now, summing the squares of the two shorter sides:
\[ 40^2 + 32^2 = 1600 + 1024 = 2624 \]
Now we compare:
\[ 2500 \neq 2624 \]
Since \(50^2\) is not equal to \(40^2 + 32^2\), triangle DEF is not a right triangle.
Thus, the correct response is:
No, triangle DEF is not a right triangle.