The length of a rectangle is 6.7 cm more than 2 times the width. If the perimeter of the rectangle is 57.2 cm, what are its dimensions?

Question

substution or elimination 2 equations

 

Answer 1

 Let width of rectangle be x centimeters and length = 2x + 6.7centimeters

 

Therefore the perimeter is   2( x + 2 x +6.7)-= 57.2

                                         2( 3x + 6.7)        = 5.72

                                           6x + 13.4          = 57.2

                                    Subtract 13.4 from both sides

                                          6x                      = 43.8

                                     Divide both sides by 6

                                            x                       =  7.3  (width)

                                  and   length = 2x +6.7  = 14.6 + 6.7 = 21.3

                   Dimensions are length = 21.3 cm  and width is 7.3 cm

       

Answer 2

draw a rectangle. mark the 2 short sides as "w"

 

and the 2 long sides as "2w + 6.7"

 

so now you have 2 w's, and 2 "2w + 6.7"s, which are all goig to add up to 57.2

 

So really you have 6w + 6.7 + 6.7; or 6w + 13.4 = 57.2

 

which means 6w by itself is 57.2 - 13.4, or 43.8

 

So 6w = 43.8  Divide both by 6 and you get w = 7.3

 

If w = 7.3, then 2 x 7.3, plus 6.7, = 21.3

 

2 x 21.3 = 42.6, and 2 x 7.3 = 14.6...

 

42.6 + 14.6 is... 57.2  :-)

 

Hope that helps!!

 

Matt