The base of the rectangle is 3 less than twice the height. If the area is 135 square inches, find the dimensions of the rectangle.

We'll note the height as x and the base as 2x -
3.

We'll calculate the area of the rectangle as the product
of the base and height:

A =
x(2x-3)

We know the value of the area and we'll substitute
in the relation above:

135 =
x(2x-3)

We'll remove the
brackets:

135 = 2x^2 -
3x

We'll subtract 135 both sides and we'll use the
symmetric property:

2x^2 - 3x - 135 =
0

We'll apply the quadratic
formula:

x1 = [3+sqrt(9 +
1080)]/4

x1 = (3+33)/4

x1 =
9

x2 = (-30)/4

x2 =
-7.5

Since a measure of a side cannot be negative, the
value -*7.5 will be rejected.

The height is 9
inches and the base is 2*9 - 3 = 15 inches.