Problem E

Parallelogram Askew

Parallelogram \(PQRS\) is positioned such that \(P\) lies on the positive \(y\)-axis, \(S\) lies on the positive \(x\)-axis, and \(Q\) and \(R\) lie in the first quadrant.

If vertices \(P\), \(Q\), and \(S\) are located at \((0,30)\), \((k,50)\) and \((40,0)\), respectively, and the area of \(PQRS\) is \(1340\text{ units}^2\), determine the coordinates of \(Q\) and \(R\).