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UKMT Grey Kangaroo, 2025

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In the rectangle $PQRS$ , the points $T$ and $U$ are marked on side $SR$ as shown, so that $\angle RUQ = \angle STP = 45^\circ$ and $PQ + UT = 20\text{cm}$ . What is the length of $QR$ ?

(A) $4\text{ cm}$ (B) $6\text{ cm}$ (C) $8\text{ cm}$ (D) $10\text{ cm}$ (E) $12\text{ cm}$

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