Question

Find a Pythagorean triplet in which one number is 12

Answer 1

$m \: sq - 1 = 12 \\ m \: sq = 12 + 1 = 13 \\ 2m = 7 \\ 12m = 6 \\ m \: sq - 1 = 36 - 1 = 35 \: and \: m \: sq + 1 = 36 + 1 = 37 \\ therefore \: the \: required \: triplet \: is \: 12 \: 35 \: 37$

Answer 2

SOLUTION

If we take m² - 1=12

Then, m² = 12 +1=13

Then the value of m will not be a integer.

So, we try to take m² + 1 = 12 .Again m²=11 will not give an integer value for m.

So, let's take 2m=12

Then m=6

Thus, m² -1=36 -1 =35 and m² + 1=36 +1 =37

Therefore, the required triplet is 12,35,37

NOTE

All Pythagorean triplet may not be obtained using this form. For example another triplet 5,12,13 also has 12 as a member

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