Question

Write the Pythagorean triplet whose smallest member is 22

Answer 1

The formula to find the pythagorean triplet is

1. 2m = 22

m = 22/2

m = 11

2. m square + 1

11 square + 1

= 121 + 1

= 122

11 square - 1

= 121 - 1

= 120

So pythagorean triplets are 21,122 and 120

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Answer 2

Answer:

Pythagorean triplet whose smallest member is 22,120,122.

Step-by-step explanation:

Pythagorean triples are $a^{2}+b^{2} =c^{2}$ where a, b and c are the three positive integers. These triples are represented as $(a,b,c).$ Here, $a$ is the perpendicular, $b$ is the base and $c$ is the hypotenuse of the right-angled triangle. The most known and smallest triplets are (3,4,5).

For any natural numbers $m > 1$,$2m,m^{2} -1,m^{2} +1$ form a Pythagorean triplet.

Take $m^{2} +1=22,$ then $m^{2} =21$.

The value of m will not be an integer.

Now take, $m^{2} -1=22$ then

$m^{2} =23$

Again the value of m will not be an integer.

Let take $2m=22$

$m=\frac{22}{2} \\\\m=11$

$\Rightarrow 2m=2\times 11=22$

So,

$m^{2} -1=11^{2}-1\\=121-1\\=120$

$m^{2} +1=11^{2}+1\\= 121+1\\=122$

Therefore, the Pythagorean triplets are $22,120,122.$

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