If the width is w then the length=w+17 and the diagonal length=w+34.
So using Pythagoras we have:
(w+17)2+w2=(w+34)2,
w2+34w+289+w2=w2+68w+1156,
w2-34w-867=0=(w+17)(w-51), so w (width)=51cm, (diagonal=85cm,) length=68cm.
NOTE: 867=3×172, so the factors are 3, 17, 51, 289. The difference of two of these is 34 (=51-17) which is the magnitude of the coefficient of the middle term of the quadratic, enabling us to easily factorise.