Question

A rectangular deck

is 12 ft by 14 ft. When the length and width are increased by the same amount very becomes 280 squares ft. By how much were the dimensions increased ?

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 = (-b \pm √(b^2 - 4ac))/(2a)`


`x = (-26 \pm √(26^2 - 4(1)(-112)))/(2(1))`


`x = (-26 \pm √(676 + 448))/(2)`


`x = (-26 \pm √(1124))/(2)`


`x = (-26 \pm 2√(281))/(2)`


`x = -13 \pm √(281)`


`x \approx -29.76` or
`x \approx 3.76`

We discard the negative answer.

Answer:

Exact:

`(-13 + √(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.