If one of the pythagorean triplet is 96 then find the other.
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If the number is odd: Square the number N and then divide it by 2. Take the integer that is immediately before and after that number i.e. (N2/2 -0.5) and (N2/2 +0.5). ...
If the number is even: Take the half of that number N and then square it. Pythagorean triplet= N, (N/2)2-1, (N/2)2+1.
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There are only three types of Pythagorean triples that could exist given a number.
The first type is where the triple is a multiple of a smaller Pythagorean triple. For example, 6–8–10 is a multiple of 3–4–5. However, 5 is a prime number and so no such triples exist that include 5.
The second type is when the triple is a leg. As such, odd numbers and even numbers have two different methods of generating such a Pythagorean triple. With an even number, you square it, divide it by 4, and take one integer on each side of this value. However, 5 is not an even number so this is not of use. With an odd number, you square it, divide it by 2, and use the two closest numbers to that value. For example, with 7, you get 24 and 25. If you try this with 5, you get 12 and 13.
The third type is when the number given is the hypotenuse. As such, you reverse the processes described in the previous paragraph. To achieve one possible set, you get one leg by subtracting 2 (yielding 3 in this case) and you get the other by subtracting by 1 (getting 4), multiplying by 4 (getting 16), and taking the square root (which in this case yields 4). To achieve another possible set, you get one leg by subtracting 1 (getting 4), and then you get another by subtracting 0.5 (getting 4.5), multiplying by 2 (getting 9), and taking the square root (getting 3). In this case, both methods yield a 3–4–5 triangle.
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The first type is where the triple is a multiple of a smaller Pythagorean triple. For example, 6–8–10 is a multiple of 3–4–5. However, 5 is a prime number and so no such triples exist that include 5.
The second type is when the triple is a leg. As such, odd numbers and even numbers have two different methods of generating such a Pythagorean triple. With an even number, you square it, divide it by 4, and take one integer on each side of this value. However, 5 is not an even number so this is not of use. With an odd number, you square it, divide it by 2, and use the two closest numbers to that value. For example, with 7, you get 24 and 25. If you try this with 5, you get 12 and 13.
The third type is when the number given is the hypotenuse. As such, you reverse the processes described in the previous paragraph. To achieve one possible set, you get one leg by subtracting 2 (yielding 3 in this case) and you get the other by subtracting by 1 (getting 4), multiplying by 4 (getting 16), and taking the square root (which in this case yields 4). To achieve another possible set, you get one leg by subtracting 1 (getting 4), and then you get another by subtracting 0.5 (getting 4.5), multiplying by 2 (getting 9), and taking the square root (getting 3). In this case, both methods yield a 3–4–5 triangle.
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