A Nearly Pythagorean Triangle (abbreviated as "NPT'), is an integer-sided triangle whose square of the longest side, which we will call as its 'hypotenuse', is 1 more than the sum of square of the shorter sides. This means that if c is the hypotenuse and a and b are the shorter sides, , satisfies the following equation:
where:
The smallest is the triangle , with . Other examples are , , and .
Unfortunately, unlike Pythagorean Triangles, a 'closed formula' for generating all possible 's, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with 's with a known ratio of the shorter sides: .
Given the value of r, find the with the second smallest perimeter. For example for , that is , the smallest perimeter is , while the second smallest perimeter is , for the with dimensions . Please present your output as vector , where a is the smallest side of the , and c is the hypotenuse.
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George Berken Nikolaos Nikolaou GeeTwo Mehdi Dehghan

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