Straight Lines

Geometry Level 3

Let $$ABCD$$ be a parallelogram, the equations of whose diagonals are $$AC: x+2y-3 =0$$ and $$BD: 2x + y - 3 = 0$$. If the length of the diagonal $$AC=4$$ units and the area of the parallelogram $$[ABCD] = 8$$ square units, what is the length of the longer side of the parallelogram?

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