## Ken's POTW

Quadrilaterals

A quadrilateral is a polygon with four sides. I am interested in finding
a few representative quadrilaterals (ABCD) with all the following
characteristics:
- All four sides are integers (AB, BC, CD, DA).
- The two diagonals (lines between opposite vertices; AC, BD) are integers.
- The above six integers are all distinct.
- The perimeter of the quadrilateral is a minimum.

- Special Case 1:
- The quadrilateral contains any angles to meet the requirements.

- Special Case 2:
- The quadrilateral contains two right angles, adjacent to each other
(DAB, CDA).

- Special Case 3:
- The quadrilateral contains two right angles, opposite one another
(DAB, BCD).

Source: Original.

Solution

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