Question

Find the pythagorean triplet in which one number is 12

Answer 1

12 , 13 and 5 is a Pythagorean triplets
consider
${13}^{2} = {5}^{2} + {12}^{2}$
$169 = 25 + 144$
$169 = 169$
LHS = RHS

Answer 2

Step-by-step explanation:

Given:

• One number of Pythagorean triplet is 12.

To Find:

• What is the Pythagorean triplet?

Solution: For any natural number m the Pythagorean Triplet = 2m , m² – 1 , m² + 1

Let m = 6

∴ 2m = 12

→ m = 12/2

→ m = 6

• Other numbers will be •

$\implies{\rm }$ m² – 1

$\implies{\rm }$ 6² – 1

$\implies{\rm }$ 6 x 6 – 1

$\implies{\rm }$ 36 – 1

$\implies{\rm }$ 35

And,

$\implies{\rm }$ m² + 1

$\implies{\rm }$ 6² + 1

$\implies{\rm }$ 6 x 6 + 1

$\implies{\rm }$ 36 + 1

$\implies{\rm }$ 37

∴ The other two numbers of the Pythagorean Triplet are 35 and 37.

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★ Note :- All Pythagorean triplet may not be obtained by using this form. For example 12 is also a member of another triplets 5,12,13 or 9,12,15 or 12,16,20