Polynomial function word problem

Question

The length of a rectangular field is 5 ft. more than its width. A pathway is constructed around the field with a width of 2ft. Write a polynomial function that models the area of the field with the pathway. And what is the area of the field alone if the rectangular field including the pathway has an area of 176 square feet (sq. ft.)? Explain solution pleaseee.

Answer 1

A_field = w(w + 5)

A_{field + path} = (w + 4)(w + 9) 2 feet added on each side

176 = (w + 4)(w + 9)

Can you solve for w and answer?