Question

The Pythagorean triplet whose smallest number is 6 is _____. Choose the correct answer to fill in the blanks.

• A. 6, 7, 5
• B. 7, 9, 2
• C. 6, 8, 10
• D. 6, 11, 10

Answer 1

The correct option is C 6, 8, 10

For any natural number m$>$1, the Pythagorean triplet adheres to $(2m{)}^2+(m^2-1{)}^2=(m^2+1{)}^2$.
$\because$ smallest number is 6, $2m=6$ or $m=3$.
$m^2+1=3^2+1=9+1=10$
$m^2-1=3^2-1=9-1=8$
So, the Pythagorean triplet is 6, 8, 10.