The area of a rectangle is 21 ft2 , and the length of the rectangle is 1 ft less than twice the width. Find the dimensions of the rectangle.

Question

need length and width.

Answer 1

Length is 1 less than twice the width

 

W = width  ;  2W - 1 = length

 

Area = 21 ft.²

 

Area = length times width

 

21 = (2W - 1)W

 

21 = 2W² - W

 

0 = 2W² - W - 21

 

Factoring

 

0 = ( 2W - 7 ) ( W + 3)

 

Set factors equal to 0

 

2W - 7 = 0  ;  W + 3 = 0

 

       W = 7/2  ;  W= -3  (width can not be a negative number)

 

Width = 7/2 ft. and length = 6 ft.

Answer 2

Hi Katherine,

 

Let width ofa rectangle be w ft

     length =( 2w-1) ft

 

Area of a rectangle = length* width

 

                             =(2w-1)w = 21

                                 2w² -w-21=0

                                 2w² -7w+6w-21=0

                                  w(2w-7)+3(2w-7) =0

                                   (2w-7) (w+3) =0

                                    2w-7=0    or   w+3=0

                                       w=3.5   or w=-3   which is negative, not possible so

  width = 3.5 ft   , length = 2w-1 =6 ft