The base of the rectangle is 3 less than twice the height If

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.

Solution

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.