Question

Why must one leg of a triangle that the Pythagorean triple represents need an even-numbered length?

Answer 1

Most of the square numbers are even.so if we need to find root over we need an even number to convert it to perfect square.

See the example below

• P=3
• B=4
• H=5

$\\ \ast\bull\rm\longmapsto H^2=P^2+B^2$

$\\ \ast\bull\rm\longmapsto H^2=3^2+4^2$

$\\ \ast\bull\rm\longmapsto H^2=9+16$

$\\ \ast\bull\rm\longmapsto H^2=25$

$\\ \ast\bull\rm\longmapsto H=\sqrt{25}$

$\\ \ast\bull\rm\longmapsto H=5$

Some other triplets are

• (6,8,10)
• (5,12,13)
• (8,15,17)