Question 390634
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Hi,         
Let w ,(w+7ft),(w+9ft)represent the width,length and diagonal respectively
Using the Pytahgorean Theorem
 w^2  + (w+7)^2 = (w+9)^2
 w^2 + w^2 + 14w + 49 = w^2 + 18w + 81
   w^2 -4w - 32 = 0
factoring
 (w-8)(w+4) = 0
  (w+4) = 0
    w = -4  Tossing out negative solution for length
  (w-8) = 0
      w = 8ft,  the width of the rectangle   (length=15ft, diagonal=17ft)

CHECKING our Answer
   64 + 225 = 289