Step 1 :The problem states that the backyard is a quadrilateral with opposite sides parallel and equal in length. This means that the backyard is a parallelogram. In a parallelogram, opposite sides are equal.
Step 2 :Therefore, if one side is \(18.288\) meters, the opposite side is also \(18.288\) meters. Similarly, if another side is \(15.24\) meters, its opposite side is also \(15.24\) meters.
Step 3 :To find the perimeter of the parallelogram, we add up the lengths of all the sides: \(18.288 + 18.288 + 15.24 + 15.24\).
Step 4 :By calculating the above expression, we get the perimeter as \(67.056\) meters.
Step 5 :Final Answer: The perimeter of the property is \(\boxed{67.056}\) meters.