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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