To find a new Pythagorean triple that contains 183 using the given triple (11, 60, 61), we can use the property of scaling a Pythagorean triple.
We know that if (a, b, c) is a Pythagorean triple, then (ka, kb, k*c) is also a Pythagorean triple for any integer k.
First, we need to determine the factor \( k \) such that one of the elements in the new triple is 183.
Given that 61 is the largest number in the original triple:
To make one of the elements equal to 183 from 61, we can set: \[ k \times 61 = 183 \]
Solving for \( k \): \[ k = \frac{183}{61} = 3 \]
Now we can multiply the original triple by 3:
- \( 3 \times 11 = 33 \)
- \( 3 \times 60 = 180 \)
- \( 3 \times 61 = 183 \)
Thus, the new Pythagorean triple is (33, 180, 183).
The new Pythagorean triple is (33, 180, 183).
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