Length exceeds width by 2 feet. When each dimension is increased by 2 feet the area increases by 48 square feet. Find the dimensions.

We'll put the width as
x.

We'll put the length as x +
2.

The area of the rectangle is theproduct of length and
width.

A = x(x+2) (1)

We'll
increase dimensions by 2 feet:

The length will become x + 2
+ 2 = x + 4

The width will become x +
2.

The area is increasing also by 48 sq.
feet.

48 + A = (x+2)(x+4)
(2)

We'll substitute A by
(1):

48 + x(x+2) =
(x+2)(x+4)

We'll move all terms in x to the left
side:

x(x+2) - (x+2)(x+4) + 48 =
0

x^2 + 2x - x^2 - 6x - 8 + 48 =
0

We'll combine and eliminate like
terms:

-4x + 40 = 0

-4x =
-40

x = 10

The
width is of 10 units and the length is of 12 units: l=12 units; w=10
units.