Question

True or false



A triangle with the sides 5,7 and √74
is a Pythagorean triple why or why not

(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 it follows the Pythagorean theorem, which states that for a right triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

1. Identify the longest side:
- Here, \( \sqrt{74} \approx 8.6 \) which is the longest side.

2. Check the Pythagorean theorem:
\[
\text{hypotenuse}^2 = 5^2 + 7^2
\]
\[
\sqrt{74}^2 = 5^2 + 7^2
\]
\[
74 = 25 + 49
\]
\[
74 = 74
\]

Since the equation holds true, the triangle with sides \(5\), \(7\), and \(\sqrt{74}\) satisfies the condition of being a right triangle.

**Therefore, the statement is True**.