Problem D

Square Parts

Square \(PQRS\) has \(W\) on \(PQ\), \(U\) on \(QR\), \(T\) on \(PS\), and \(V\) on \(TU\) such that \(QUVW\) is a square, and \(PWVT\) and \(RSTU\) are rectangles.

The side length of square \(PQRS\) is \(9\) cm, and \[\text{area of } QUVW - \text{ area of } RSTU = \text{ area of } RSTU - \text{ area of }PWVT\] If square \(QUVW\) has side length equal to \(x\) cm, determine the value of \(x\) and the areas of rectangles \(PWVT\) and \(RSTU\).