Original length: 14 ft. New length x + 14.
Original width: 12 ft. New width x + 12.
New area:
[tex] A = LW [/tex] or [tex] LW = A [/tex]
[tex] (x + 14)(x + 12) = 280 [/tex]
[tex] x^2 + 14x + 12x + 168 = 280 [/tex]
[tex] x^2 + 26x - 112 = 0 [/tex]
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-26 \pm \sqrt{26^2 - 4(1)(-112)}}{2(1)} [/tex]
[tex] x = \dfrac{-26 \pm \sqrt{676 + 448}}{2} [/tex]
[tex] x = \dfrac{-26 \pm \sqrt{1124}}{2} [/tex]
[tex] x = \dfrac{-26 \pm 2\sqrt{281}}{2} [/tex]
[tex] x = -13 \pm \sqrt{281} [/tex]
[tex] x \approx -29.76 [/tex] or [tex] x \approx 3.76 [/tex]
We discard the negative answer.
Answer:
Exact:
[tex] (-13 + \sqrt{281})~ ft [/tex]
Approximate:
[tex] 3.76 ~ft [/tex]
