The base of a rectangle is three less than twice the height. Determine the dimensions of the rectangle if the area is 135 square inches.

Let the height of the rectangle be H. Now the base is
three less than twice the height or base is 2H-3.

The area
of the rectangle is base* height = H*( 2H-3)

H*( 2H-3) =
135

=> 2H^2 - 3H
=135

=> 2H^2 - 3H - 135
=0

The roots of the equation
are

H1 = [3 + sqrt(9+1080)] /
4

= (3 + 33)/4

= 36 /
4

=9

H2 = [3 - sqrt(9+1080)] /
4

= (3 - 33)/4

= -30 /
4

=-7.5

Now the dimension of a
rectangle cannot be negative, so we eliminate -7.5

The
Height then is 9 and the base is 135/ 9
=15

The dimensions of the rectangle are 9 and
15 inches.