Question

Given that
(11,60, 61) is a Pythagorean triple,
use
(11, 60, 61) to find a new Pythagorean triple that contains 183. (1 point)
The new Pythagorean triple is ( ,
),183).

Answer 1

To generate a new Pythagorean triple containing 183 using the given Pythagorean triple \((11, 60, 61)\), we can use a scaling factor.

Since \(183\) can be thought of as a multiple of \(61\), we can find a scaling factor by dividing \(183\) by \(61\):

\[
k = \frac{183}{61} = 3
\]

Now, we multiply the components of the original Pythagorean triple by \(3\):

\[
(11 \times 3, 60 \times 3, 61 \times 3) = (33, 180, 183)
\]

Thus, the new Pythagorean triple that includes \(183\) is:

\[
(33, 180, 183)
\]

Final answer:
The new Pythagorean triple is \((33, 180, 183)\).