find the pythagorean triplet whose one number is 12
Answers
Answer:
Pythagorean triplets are 12, 35, 37.
Step-by-step explanation:
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).
Pythagorean triplet= N, (N2/2 -0.5), (N2/2 +0.5)
Example: Take number N=3.
On squaring the number, we get 9.
Now take the half of it. 9/2= 4.5
The integer immediately before 4.5= 4; the integer immediately after 4.5= 5
Therefore, the triplet is 3, 4, 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
Example: Take number N=8
Half of N=4.
Pythagorean triplet= 8, (42-1), (42+1) i.e. 8, 15, 17
Note: If a, b, c is a Pythagorean triplet, then ka, kb, kc will also form a Pythagorean triplet; where k= integer. As (3, 4, 5) is a triplet, (6,8,10), (9,12,15),(12,16,20),...(30,40,50), all these will also be triplets.
Commonly Used Pythagorean Triplets:
Three numbers which satisfy Pythagorean Theorem form a Pythagorean Triplets. Some commonly used Pythagorean triplets asked in the exams directly or indirectly are:
3,4,5; 5,12,13; 7,24,25; 9,40,41; 11,60,61; 12,35,37; 8,15,17; 28,45,53; 20,21,29; 16,63,65
12,35,37 are the pythagorean triplets of 12