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Since the parallel sides of a parallelogram are equal in length, we can set up an equation to solve for the value of x.
Perimeter = 2(BC) + 2(AB)
36 = 2(4x) + 2(2x)
36 = 8x + 4x
36 = 12x
x = 3
Therefore, the shorter side of the parallelogram is 2x = 2(3) = 6 yards.