To determine if triangle DEF with sides measuring 50, 40, and 32 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 (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
First, identify the sides:
- The longest side (hypotenuse) is 50.
- The other two sides are 40 and 32.
Now we apply the Pythagorean theorem:
\[ 50^2 = 40^2 + 32^2 \]
Calculating each term:
\[ 50^2 = 2500 \]
\[ 40^2 = 1600 \]
\[ 32^2 = 1024 \]
Now, add \(40^2\) and \(32^2\):
\[ 40^2 + 32^2 = 1600 + 1024 = 2624 \]
Now compare:
\[ 2500 \neq 2624 \]
Since \(50^2\) is not equal to \(40^2 + 32^2\), triangle DEF is not a right triangle.
Therefore, the answer is:
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