the perimeter of a rectangle is 28 inches. the length is 6 less than 3 times the width. what is the length of the rectangle

Question

the perimeter of a rectangle is 28 inches. the length is 6 less than 3 times the width. what is the length of the rectangle 

Answer 1

We have two important pieces of information:

 

(1) "the perimeter of a rectangle is 28 inches"     So, Let L=length; W=Width;

             and this says P = 2L+2W = 28

 

(2) "the length is 6 less than 3 times the width"  That is, 

           L          =  -6       +    3   *          W

 

So, let's do the easy math:

  From the equation in (1),   L = 14 - W

 

substitute that into the equation from (2):

         14 - W = -6 + 3W

         14 -4W = -6                [subtract 3W from both sides]

            -4W = -20                [subtract 14 from both sides]

              W = 5                    [divide both sides by -4]

 

Now, use either equation [ let's use modified eq1, L=14-W] to find L:

                  L = 14 - W

                  L = 14 - 5

                  L = 9

 

Checking (very important):

  Is 2(9)+2(5)=28   ?

       18 + 10 = 28   ?

            28 = 28  ?  yes

  Is 9 = -6 + 3(5)   ?

       9 = -6 + 15   ?

         9 = 9 ?  yes