Question

Are all of the following triplets are pythagorean?

$(8,15,17)$
$(16,63,65)$
$12,16,20$

• A. Yes
• B. No
• C. Cannot be determined
• D. None

Answer 1

The correct option is A Yes

To check if the set of numbers $a,b,c$are Pythagorean triplets, we need to check if $a^2+b^2=c^2$
1) For $8,15,17$
$8^2+{15}^2=64+225=289$
and ${17}^2=289$
Hence, $8^2+{15}^2={17}^2$
2) For $16,63,65$
${16}^2+{63}^2=256+3969=4225$
and ${65}^2=4225$
Hence, ${16}^2+{63}^2={65}^2$
3)For $12,16,20$
${12}^2+{16}^2=144+256=400$
and ${20}^2=400$
Hence, ${12}^2+{16}^2={20}^2$
Thus, the given set of numbers are Pythagorean triplets.