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Problem: Parallelogram with Integer Sides and Integer diagonals

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Suppose you are given to line segments of lengths 13 and 6 respectively

Now construct a parllelogram

Of all such parallograms, find those with BOTH diagonals of integer length.

For a GSP file to animate, Click Here.

Extension:

Find other parallelograms with integer sides and integer diagonals.

Can there be a general characterization of all such parallograms?