the length of a rectangular table is 6 inches longer than twice the width.if the perimeter of the table is 600 inches. what is the length and width?

Question

math question

Answer 1

Let:

  L = length

  W = Width

 

Translate:

  "the length of a rectangular table is 6 inches longer than twice the width"     means

            L                                     =   6                    +        2   *    W          (eq1)

  "perimeter of the table is 600 inches"    means

           L+W+L+W         = 600                (eq2) (assume you know formula for perimeter)

  "what is the length and width?"      means      report L and W

 

Now, the easy math:

         2L + 2W = 600             (rewrite eq2)

        2(2W+6) + 2W = 600       (rewrite eq1 and substitute for L in eq2)

         4W + 12 + 2W = 600           (distribute)

          6W + 12 = 600                  (collect terms)

           6W = 588                     (subtract 12 from each side)

            W = 98

 

Substitute that value of W into either equation (which is easier?):

          L = 6 + 2(98)

          L = 6 + 196

          L = 202

 

Checking (very important):

  Is   202 = 6 + 2(98)   ?

        202 = 6 + 196   ?

         202 = 202   ? yes

  Is   2(202) + 2(98) = 600   ?

        404 + 196 = 600  ?

           600 = 600   ? yes

Answer 2

The length of the rectangle would be

 

2w + 6 where the width is w

 

Now the perimeter of the table would be

 

2 length + 2 width 

 

So, 

 

2 (2w + 6) + 2 w = 600

 

6w + 6 = 600

 

6w = 594

 

W = 99 in and the length is

 

2 (99) + 6 = 204 in