dimensions

Question

The length of a rectangle is 2
meters less than twice the width. If the area of the rectangle is 220
square? meters, find the dimensions.

Answer 1

 

Let W = width of rectangle

Let 2W-2 = length of rectangle ... 2 less than twice the width

 

     Area = Length • Width

      220  = (2W - 2)(W)

      220 = 2W² - 2W

      0 = 2W - 2W - 220

 

Simplify by dividing both sides by 2

 

      0 = W² - W - 110

 

Factoring and Using the zero product property

 

      0 = (W + 10)(W - 11)

 

      W + 10 = 0 ... W = -10 ... discard;  can]t have a negative dimension

 

      W - 11 = 0 ... W = 11

 

The Width is 11 meters.

The Length is 2W - 2 = 2(11) -2 = 22 - 2 = 20

The Length is 20 meters.

 

CHECK:

   

    Area = Length • Width

     220 = 20(11)

 

     220 = 220