Question

Determine if the following lengths are Pythagorean triples: $9,40$ and $41$.

Answer 1

The longest side of the triangle is called hypotenuse. According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the square of the two other sides.

$\therefore {41}^2={40}^2+9^2$

$\Rightarrow {40}^2+9^2=1600+81=1681$

$\Rightarrow {41}^2=1681$

$\therefore 1681=1681$

Hence these length are Pythagorean triples.