write two Pythagorean triplets each having one number as 5
Answers
Answer:
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.
Therefore, the only two triples that contain the number 5 are (5,12,13) and (3,4,5).
Below is some more fun for the people who are wondering why I wrote such a long answer:
You could use this analysis for any number. For example, given the number 28, you must first find Pythagorean triples containing all it’s multiples and then multiplying them. The triples include 7–24–25, which gets multiplied to become 28–96–100, and 3–4–5, which gets multiplied to become 21–28–35. Secondly, you find the triple with 28 as its leg. Square it (getting 784), divide it by 4 (getting 196), and get the two nearest integers (195 and 197). 28–195–197 is another multiple. Thirdly, you get the triples for which 28 is a hypotenuse. Neither methods creates an integer triple for which 28 is a hypotenuse. Therefore, 28 is only included in 3 triples: 28–96–100, 21–28–35, and 28–195–197.
Answer:
1) 3 , 4 and 5
5² = 4²+3²
25 = 16+9
25= 25
2) 5, 12 and 13
13² = 12²+5²
169= 144+25
169 = 169.
hope it helps you mate
please thank and mark my answer as brainliest.