The length of a rectangle is 6 centimeters less than two times its width. The area of the rectangle is 216 square centimeters. What are the dimensions of the rectangle?

W=12 cm, L=18 cm

Step-by-step explanation:

given:

The length of a rectangle is 6 centimeters less than two times its width.

The area of the rectangle is 216

square centimeters.

find:

What are the dimensions of the rectangle?

solution:

area of a rectangle = Length(L) x Width(W)

where

A = 216 cm²

L =  2W - 6

plugin values into the formula

216 = (2W - 6) W

216 = 2W² - 6W

rearrange:

2W² - 6W - 216 = 0

solve W by using quadratic equation:

           - (-6) ±

W = -------------------------------------------

                                 2 (2)

W = 12;  W = -9

solve L: substitute W=12 into L =  2W - 6

L =  2W - 6

L = 2(12) - 6

L = 18 cm

therefore:

the dimensions of the rectangle is W=12 cm, L=18 cm