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Australian AMC 2010 - Junior Question 27

AMC AUSTRALIA · Australian AMC 2010 - Junior

Question 27

Two overlapping squares, $QTVU$ and $SXYZ$, are drawn inside the rectangle $PQRS$ so that the perimeters of the three shaded rectangles are equal.

Question illustration

If the lengths of the sides of $PQRS$ are 20 cm and 22 cm, what is the sum of the perimeters, in centimetres, of the squares $QTVU$ and $SXYZ$?