Question

A Pythagorean triplet whose smallest member is $8$, is:

• A. $8,15,18$
  
• B. $8,13,16$
• C. $8,14,17$
• D. $8,15,17$
  

Answer 1

The correct option is D $8,15,17$

We can get Pythagorean triplet by using general form $2m,m^2-1,m^2+1$
Let us first take

$m^2-1=8$
So, $m^2=8+1=9$
Which gives $m=3$
Therefore $2m=6$ and $m^2+1=10$

The triplet is thus $6,8,10$, but $8$ is not the smallest member of this triplet.

So let us try

$2m=8$
then $m=4$
We get $m^2+1=16-1=15$
and $m^2+1=16+1=17$
The triplet is $8,15,17$ with $8$ as the smallest member.

Hence, option $D.$