Question

what is the Pythagorean triple
for the lengths 60,25,65
65 is the hypotenuse
60 is the vertical leg
25 is the horizontal leg

Answer 1

To verify if the lengths 60, 25, and 65 form a Pythagorean triple, we can use the Pythagorean theorem, which states that in a right triangle:

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

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two legs.

In your case:

- \( a = 25 \) (horizontal leg)
- \( b = 60 \) (vertical leg)
- \( c = 65 \) (hypotenuse)

Now we can plug the values into the Pythagorean theorem:

\[
25^2 + 60^2 = 65^2
\]

Calculating each term:

\[
25^2 = 625
\]
\[
60^2 = 3600
\]
\[
65^2 = 4225
\]

Now adding \( 25^2 \) and \( 60^2 \):

\[
625 + 3600 = 4225
\]

Since both sides of the equation are equal:

\[
4225 = 4225
\]

This confirms that \( 60, 25, \) and \( 65 \) indeed form a Pythagorean triple, with \( 65 \) as the hypotenuse.