Question

True or false



A triangle with the sides 5,7 and 74−−√
is a Pythagorean triple.

(1 point)
Responses decimals are not integers

True
True

False

Answer 1

To determine whether the triangle with sides \(5\), \(7\), and \(\sqrt{74}\) is a Pythagorean triple, we will check if the Pythagorean theorem holds. A Pythagorean triple is a set of three positive integers \(a, b, c\) such that \(a^2 + b^2 = c^2\), where \(c\) is the longest side.

First, we identify the longest side:
- The sides are \(5\), \(7\), and \(\sqrt{74}\).
- Since \(\sqrt{74} \approx 8.6\), we can see that \(\sqrt{74}\) is the longest side.

Now, we need to check if:
\[
5^2 + 7^2 = (\sqrt{74})^2
\]

Calculating each side:
- \(5^2 = 25\)
- \(7^2 = 49\)
- So, \(5^2 + 7^2 = 25 + 49 = 74\)
- On the right side, \((\sqrt{74})^2 = 74\)

Since both sides are equal, \(5^2 + 7^2 = (\sqrt{74})^2\) holds true.

Therefore, the statement is **True**, and the triangle with sides \(5\), \(7\), and \(\sqrt{74}\) is a Pythagorean triple.