The area of a rectangular garden is 54 square meters.The width is 3 meters longer than one-third of the length. Find the length and width of the garden.

Question

 That is all.

Answer 1

 

Hi Kahlee,

 

The statement that the width is 3 meters longer than one-third of the length

 

can be put into the following expression.

 

     W = (1/3)L + 3

 

where W and L represent the width and length, respectively.

 

As the area of a rectangle is given by the product of W and L,

 

     Area = W·L

 

             = ((1/3)L + 3)·L

 

             = (1/3)L² + 3L

 

             = 54

 

     (1/3)L² + 3L - 54 = 0

 

     L² + 9L - 162 = 0

 

     (L - 9)(L + 18) = 0

 

     L = 9 or -18

 

As L needs to be positive,

 

L = 9 can be the only meaningful answer.

 

If we plug L = 9 into the following,

 

     W = (1/3)L + 3

 

         = (1/3)·9 + 3

 

         = 6

 

∴ Width = 6, Length = 9