Triangle WAR is a right-angled triangle with one leg 28 units (AR).

The other leg,  WA,  is  WA = CW + AC = 15+6 = 21 units long.

So, triangle WAR is (3,4,5) right angled triangle (since 21:28 = 3:4).


Triangle WDC is a right-angled triangle, similar to triangle WAR
(they have one common acute angle CWD).
Hence, triangle WDC also is (3,4,5)-right-angled triangle.
Its hypotenuse WC is 15 units long - hence, triangle WDC has the sides
WD = 9 units and CD = 12 units.


Triangle CAO is a right-angled triangle, similar to triangle WAR
(since CO is parallel to WR).
Hence, triangle CAO is (3,4,5)-right-angled triangle.
Its leg CA is 6 units long - hence, its hypotenuse CO is 10 units long.


Thus the sides CD and CO of the rectangle COLD are 12 and 10 units, respectively.
Then its diagonal is   =  =  = 15.62049935... 


ANSWER.  The length of the diagonal of rectangle COLD is  = 15.62049935...