First let's model the carpet as a rectangle.
The diagonal of a rectangle is given by:
d = root ((L) ^ 2 + (W) ^ 2)
Where,
L = long
W = width.
Clearing the width we have:
d = root ((L) ^ 2 + (W) ^ 2)
d ^ 2 = (L) ^ 2 + (W) ^ 2
(W) ^ 2 = (d) ^ 2- (L) ^ 2
W = root ((d) ^ 2- (L) ^ 2)
Substituting the values
W = root ((root (89)) ^ 2- (8) ^ 2) = 5
answer
The width of the carpet is
5 feet