L = 4

W = 12

A = L*W = 4*12 = 48

We want double the area, which is:

2A = 2*48 = 96

Now, we want to change the length and width to double the area, however, we will be increasing the length and width by the same amount. We'll call this amount the "width" which we'll let equal x.

L1 = L + x

W1 = W + x

A1 = L1*W1 = (L + x)(W + x) = L*W + Lx + Wx + x^2

We want A1 to equal 2*A, so, if A1 = 96, L = 4, W = 12, then the equation becomes:

96 = 48 + 4x + 12x + x^2

x^2 + 16x - 48 = 0

x = (-16 +/- sqrt(448))/2 = -8 +/- 4sqrt(7)

But since the length must be positive, we have that:

x = 4sqrt(7) - 8 = 2.583

2. Vanessa built a rectangular pen for her dogs. She used an outside wall of the garage for one of the pen sides. She had to buy 20m of fencing in order to build the other sides of the pen. Find the dimensions of the pen if the area is 48m^2 (squared).

P = W + 2L = 20 --> W = 20 - 2L

A = W*L = 48 --> 48 = (20 - 2L)L = 20L - 2L^2

2L^2 - 20L + 48 = 0

2(L^2 - 10L + 24) = 0

2(L - 12)(L + 2) = 0

L = 12, -2

Since length must be positive, we have that:

L = 12

W = 20 - 2(12) = -4

Did I make a mistake? I'll come back and check my work in a second.