Answer:
The length is 14ft, and the width is 2ft.
Step-by-step explanation:
Recall that area of a rectangle is given by
[tex]A=LW[/tex]
From the question, the area of the rectangular wall of a barn is 28 ft² .
The length is 12 ft longer than the width, so
L=W+12
We substitute into the area formula to get:
[tex]28 = w(w + 12)[/tex]
We expand to get:
[tex]28 = {w}^{2} + 12w[/tex]
[tex] {w}^{2} + 12w - 28 = 0[/tex]
Split the middle term:
[tex] {w}^{2} + 14w - 2w - 28 = 0[/tex]
Factor to get:
[tex]w(w + 14) - 2(w + 14) = 0[/tex]
[tex](w + 14)(w - 2) = 0[/tex]
[tex]w = -1 4 \: or \: w = 2[/tex]
Since the width is always positive , w=2ft
The length will then be,
[tex]l = 12 + 2 = 14ft[/tex]
