Enigma 1427: Equal lengths
From New Scientist #2588, 27th January 2007
I challenged Harry and Tom to draw this diagram, with the angles ABD, BEC and CED each 90° and each side of the three triangles an integral number (less than 40) of centimetres long.
They each managed to do this.
In Harry’s version (AB+BC) was the same length as (AD+DC); in Tom’s version (AB+BE) was the same length as (AD+DE); CE was the same length in both versions.
What was the length of the perimeter of the quadrilateral ABCD in (a) Harry’s version, (b) Tom’s version?