Question

Find a Pythagorean triplet whose one number is 12.

Answer 1

Hint: In order to find a Pythagorean triplet , firstly find the value of m , and then place the value of m in the other two equations . After simplifying them you will obtain the required solution. Also go through the definition of Pythagorean triplet for better understanding.

Complete step by step solution:
 Here we know that common form of Pythagorean triplet is supposed to be
\[\left( {2m,{m^2} - 1,{m^2} + 1} \right)\]
So, \[2m = 12\]
By sending 2 right and side we get,
\[
  m = \dfrac{{12}}{2} \\
  m = 6 \;
\]
Similarly,
\[{m^2} - 1 = {6^2} - 1 = 36 - 1 = 35\]
And again similarly,
\[{m^2} + 1 = {6^2} + 1 = 36 + 1 = 37\]
Therefore as a result, the Pythagorean triplet with one number equals 12 is,
\[12,35,37\].
So, the correct answer is “\[12,35,37\]”.

Note: Pythagorean triples are the special set of integers that satisfy the Pythagoras theorem, as we all know. The Pythagoras theorem has a special relationship with the set of integer numbers. The Pythagoras theorem is satisfied not only by the set, but also by the multiples of the integer set.
Pythagorean triples always include all even numbers or two odd numbers and an even number, which is an interesting feature about them. A Pythagorean triple can't include all odd numbers or two even numbers plus an odd number.