Question

True or false   A triangle with the sides 5,7 and  74−−√  is a Pythagorean triple. (1 point) Responses True True False

Answer 1

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**.