let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

A = 98 ft^2 the area

a rectangle is 7 feet longer than it is wide:

l = w + 7

the formula for the area of rectangle is: A = l*w thus

l*w = 98

plug l = w +7 into the last equation:

(w + 7)*w = 98

by solving we find:

w = 7 m

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l = 7 + 7

l = 14 m

the width of the rectangle is 7 meters.

the length of the rectangle is 14 meters.