Write two Pythagorean triplets each having one of the numbers as 5.

Given:

A number $5$ is one number of the Pythagorean triplets.

To do:

We have to write two such Pythagorean triplets.

Solution:

One number of the Pythagorean triplets is $5$.

We know,

Pythagorean triplets $=m^2-1, 2m, m^2+1$

Here,

$m^2+1=5$

$\Rightarrow m^2=5-1=4$

$\Rightarrow m=2$

If $m=2$, then

$\Rightarrow m^2-1=2^2-1=4-1=3$

$\Rightarrow m^2+1=2^2+1=4+1=5$

Here, 5 is the hypotenuse.

If we take 5 as one of the legs, then,

We know that,

$13^2=169$

$=144+25$

$=12^2+5^2$

Therefore, $(5, 12, 13)$ is a Pythagorean triplet.

Hence, the required Pythagorean triplets are $(3, 4, 5)$ and $(5, 12, 13)$.

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Updated on: 10-Oct-2022

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