First the diagram: see attachment.Originally Posted by Chuck_3000
Now Part (a):
Now and are right triangles with hypotenuses of length
, so for :
with and integers, and trail and error shows that the pair
of lengths is one of .
The same argument applies to .
So for part (a) we have the minimum of
(each pairs is one of
but with none of the sides equal, so these sides is one of in some order, without repetition)
Also cannot be or less (trial and error shows this can't be
, and it must be greater than as it must be greater than ).
But can be .
So the minimum perimeter is .