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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