let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

A = 7280 in^2 the area of the rectangle

a rectangle has a length of 37 inches less than 7 times its width

l = 7w - 37

the area of the rectangle is 7280 square inches

A = l*w is the formula of the are of the rectangle

l*w = 7280

by replacing l= 7w - 37 in the above equation we have

(7w - 37)w = 7280

by solving the quadratic equation we find and consider only the positive roots (since w>0)

w = 35 in

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l = 7*35 - 37 = 245 - 37 = 208 in

the length of the rectangle is 208 inches.