In order to solve this equation, we must create a couple equations.
The equations of the area of the box is
[tex]A = L\times W\\A=12\times8\\A = 96[/tex]
So the original area of the box is 96, now we need to double to find our new box's dimension.
We can call this "added amount" x, so that we can solve the equation. Instead of pluggin 12 and 8 in, we will add the "x" variable.
So our new equation will look like the following
[tex]A=L\times W\\96\times2= (12+x)\times(8+x)\\[/tex]
So, now we just need to solve
[tex]A=L\times W\\96\times2= (12+x)\times(8+x)\\192=96+x^2+12x+8x\\192=x^2+20x+96\\0=x^2+20x-96\\0= (x+24) (x-4)\\X= -24, 4[/tex]
So, we have two values of X, but since we are talking about distance, we must reject the negative number. So we add 4" to each dimension of the box making the new dimensions
16x12in
