Quadrilateral Query
Geometry
Level
3
Consider quadrilateral ABCD whose diagonals are perpendicular and meet at point E.
Minimize the perimeter of ABCD where AB, BC, CD, DA, EA, EB, EC, ED are all different integers.
The answer is 176.
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1 solution
AB=25 BC=39 CD=60 DA=52 EA=20 EB=15 EC=36 ED=48 The perimeter is 176.
Here is a more accurate picture.
The yellow and blue are 3-4-5 right triangles scaled by 5 and 12 respectively.
The green and red are 5-12-13 right triangles scaled by 3 and 4 repectively.