Let A equal area, l equal length, and w equal width.
[tex]A = 320,320[/tex] sq. ft.
[tex]A = l * w[/tex]
[tex]l = 1212 + 2w[/tex]
[tex]320,320 = w(1212+2w)[/tex]
[tex]2w^2 + 1,212w - 320,230 = 0[/tex]
[tex]w^2 + 606w - 160,160 = 0[/tex]
By the quadratic formula, [tex] w =- 303 +/- \sqrt{251,969}[/tex] or [tex]w = 198.965, w = -804.965[/tex].
Clearly, width cannot be a negative number, so we restrict its domain to w > 0.
Thus, w = 198.965.
Plugging in w to original equation for l, we get [tex]l = 1,212 + 2(198.965)[/tex] = 1,609.930.
