Rectangle lengthThe lenghts of arectangle is two inches more than its width. If the lenghth is increased by four inches and the width is doubled, a...

We'll establish the dimensions of the original
rectangle:

 - the width: x

 -
the length: x + 2

The area of the original rectangle
is:

A1 = x*(x+2)

We'll
establish the dimensions of the new formed rectangle:

 -
the width: 2x

 - the length: (x + 2) + 4 = x +
6

The area of the new rectangle
is:

A2 = 2x(x+6)

We know from
enunciation that the new area is 75 more than the area of the original
rectangle.

A2 = 75 +
A1

2x(x+6) = 75 + x(x+2)

We'll
remove the brackets:

2x^2 + 12x = 75 + x^2 +
2x

We'll move all terms to one
side:

2x^2 + 12x - 75 - x^2 - 2x =
0

We'll combine like
terms:

x^2 + 10x - 75 =
0

We'll apply the quadratic
formula:

x1 = [-10+sqrt(100 +
300 )]/2

x1 = (-10+20)/2

x1 =
5

x2 = (-10-20)/2

x2 =
-15

Since the measure of a side cannot be negative, we'll
reject the second negative value.

So, the
width of the original rectangle
is:

x = 5
inches

the length: x + 2 = 7
inches