Question

What is the Pythagorean triplets whose one member is $20$?

• A. $20,97,99$
• B. $20,99,101$
• C. $20,197,199$
• D. $20,199,201$

Answer 1

Answer: (B)

$20,99,101$

For any natural numbers $m>1,2m$, $m^2-1$, $m^2+1$ forms a Pythagorean triplet.
If we take $m^2+1=20$, then $m^2=19$
The value of m will not be an integer.
If we take $m^2-1=20$, then $m^2=21$
Again the value of m will not be an integer.
Let $2m=20$
$=>m=10$
$\therefore 2m=2\cdot 10=20$
$m^2-1$ = ${10}^2-1=99$
and
$m^2+1$ = ${10}^2+1=101$
Therefore, the Pythagorean triplets are $20,99,101.$