Question

Do the following numbers make Pythagorean triplets?
(i) $8,10,17$
(ii) $8,10,12$

Answer 1

As Pythagoras theorem says $c^2=a^2+b^2$ where $c$ is the longest side of the triangle, called the hypotenuse $a$ and $b$ are other sides. So if this condition satisfies the number then they will make Pythagorean triplets.

$\left(i\right)8,10,17$

So,

${17}^2=289$

$8^2+{10}^2=64+100$

$=164$

Which means

${17}^2\ne 8^2+{10}^2$

So, these numbers will not make Pythagorean triplets.

$\left(ii\right)8,10,12$

${12}^2=144$

$8^2+{10}^2=64+100$

$=164$

Which means

${12}^2\ne 8^2+{10}^2$

So, these numbers will not make Pythagorean triplets.