Question

A rectangular deck

Answer 1

Original length: 14 ft. New length x + 14.
Original width: 12 ft. New width x + 12.

New area:

$A = LW$  or $LW = A$

$(x + 14)(x + 12) = 280$

$x^2 + 14x + 12x + 168 = 280$

$x^2 + 26x - 112 = 0$

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \dfrac{-26 \pm \sqrt{26^2 - 4(1)(-112)}}{2(1)}$

$x = \dfrac{-26 \pm \sqrt{676 + 448}}{2}$

$x = \dfrac{-26 \pm \sqrt{1124}}{2}$

$x = \dfrac{-26 \pm 2\sqrt{281}}{2}$

$x = -13 \pm \sqrt{281}$

$x \approx -29.76$   or   $x \approx 3.76$

We discard the negative answer.

Answer:

Exact:
$(-13 + \sqrt{281})~ ft$

Approximate:
$3.76 ~ft$

Answer 2

Both dimensions were increased by 127.

The other response seems more complex so probably ignore mine. I probably misinterpreted the question.