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Problem 439

Geometry Difficulty 2.2 Multiple choice CEMC Fermat · Canada · 2013

In the diagram, rectangle $PQRS$ has $PQ=30$ and rectangle $WXYZ$ has $ZY=15$ .

If $S$ is on $WX$ and $X$ is on $SR$ so that $SX=10$ , then $WR$ equals

Pick one

Official solution

Since $PQRS$ and $WXYZ$ are rectangles, then $SR = PQ=30$ and $WX = ZY = 15$ .

Since $SX=10$ , then $WS = WX-SX=15-10=5$ .

Thus, $WR = WS+SR=5+30=35$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.