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.

The sides are:
- \( a = 5 \)
- \( b = 7 \)
- \( c = \sqrt{74} \)

We first find which is the longest side. Since \( \sqrt{74} \approx 8.6 \), \( \sqrt{74} \) is the longest side.

Now, let's calculate the squares:

1. \( a^2 = 5^2 = 25 \)
2. \( b^2 = 7^2 = 49 \)
3. \( c^2 = (\sqrt{74})^2 = 74 \)

Now, we check if \( a^2 + b^2 = c^2 \):

\[
25 + 49 = 74
\]

Since this equality holds true, the sides \( 5, 7, \) and \( \sqrt{74} \) do form a Pythagorean triple.

Therefore, the answer is **True**.