Question

Find a Pythagorean triplet in which one member is 12

• A. 5, 12, 13
  
• B. 7, 12, 19
  
• C. 11, 12, 15
  
• D. 11, 12, 18
  

Answer 1

The correct option is A 5, 12, 13

If we take m${}^2$-1=12
Then m${}^2$=12+1=13
Then the value of m will not be an integer
So we try to take $m^2+1=12Againm{}^2=11$ will not give an integer value for m
So let us take 2m = 12
then m=6
Thus $m^2-1=36-1=35$ and $m^2+1=36+1=37$
Therefore the required triplet is 12, 35, 37
Note : All Phythagorean triplets may not be obtained using this form For example another triplet 5, 12, 13 also has 12 as a member