Integer Full Of Squares

 This is why they are squares in rational right angle triangle,

the squares fit exactly.

$\cfrac{1}{2}*\cfrac{204}{3}*\cfrac{6}{3}=68=2*2*17$

the squares comes from multiple factors, in this case $2*2$.

Note:  ${\cfrac{204}{3},\,\cfrac{6}{3}}$ also work for an area of 51 which has no square and so squareless.