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 find a new Pythagorean triple that includes the number 183 using the given triple (11, 60, 61), we note that we can multiply each component of the original triple by the same factor.

First, we need to determine by what factor we can multiply to include 183.

Let's calculate a multiplier \( k \):

\[
61k = 183
\]

Now, we solve for \( k \):

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

Now that we have the multiplier \( k = 3 \), we will multiply each component of the original Pythagorean triple by 3:

1. \( 11 \times 3 = 33 \)
2. \( 60 \times 3 = 180 \)
3. \( 61 \times 3 = 183 \)

Thus, the new Pythagorean triple is:

\[
(33, 180, 183)
\]

So, the new Pythagorean triple is \( (33, 180, 183) \).