Hi,



the perimeter of a rectangle lawn is 38 units

 2L + 2W = 38  or L + W = 19   and L = 19-W

if the area of the lawn is 60 units^2,

 w(19-w) = 60

   19w - w^2 = 60

     w^2 - 19w + 60 = 0

factoring

  (w-15)(w-4) = 0,  w = 15 or 4 units.  dimension of the lawn is 15units by 4 units 

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