Consider pentagon PQRST. Starting at P and moving around the pentagon, the vertices are labelled P, Q, R, S, and T, in order. The pentagon has right angles at P, Q, and R, obtuse angles at S and T, and an area of 1000 cm2. Point V lies inside the pentagon such that ZPTV, ZTVS, and ZV SR are right angles. Point U lies on TV such that ASTU has an area of 210 cm². Also, it is known that PQ = 50 cm, SR= 15 cm, and TU = 30 cm. Determine the length of PT.

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