Question

Is (5,7,74−−√)
a Pythagorean triple? Enter 1 for yes or 2 for no.(1 point)

Answer 1

To determine if the triplet (5, 7, \(\sqrt{74}\)) is a Pythagorean triple, we need to check the Pythagorean theorem, which states that for a triplet (a, b, c) to be a Pythagorean triple, the following must be true:

\[ a^2 + b^2 = c^2 \]

Here, let's assign:
- \( a = 5 \)
- \( b = 7 \)
- \( c = \sqrt{74} \)

Now we compute \( a^2 + b^2 \) and \( c^2 \):

1. Calculate \( a^2 + b^2 \):
\[
5^2 + 7^2 = 25 + 49 = 74
\]

2. Calculate \( c^2 \):
\[
(\sqrt{74})^2 = 74
\]

Since \( a^2 + b^2 = 74 \) and \( c^2 = 74 \), we have:

\[
a^2 + b^2 = c^2
\]

Thus, (5, 7, \(\sqrt{74}\)) is a Pythagorean triple.

The answer is **1** (yes).