To determine if the triangle with sides \( 5 \), \( 7 \), and \( \sqrt{74} \) is a Pythagorean triple, we need to check if the sum of the squares of the two shorter sides equals the square of the longest side.
Let's identify the longest side:
- The sides are \( 5 \), \( 7 \), and \( \sqrt{74} \).
- Since \( \sqrt{74} \approx 8.6 \), it is the longest side.
Now, we can set up the equation to check:
\[ 5^2 + 7^2 = (\sqrt{74})^2 \]
Calculating the squares:
\[ 5^2 = 25 \]
\[ 7^2 = 49 \]
\[ (\sqrt{74})^2 = 74 \]
Now add the squares of the two shorter sides:
\[ 25 + 49 = 74 \]
Since both sides are equal (\( 74 = 74 \)), we find that the triangle with these sides does indeed form a Pythagorean triple.
Thus, the statement is True.
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