Problem 18 · 2010 Math Kangaroo
Hard
Geometry & Measurement
area
In the figure, ABCD is a rectangle and PQRS a square. The area of the grey part is half as big as the area of ABCD. How long is the side PX?
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Answer: A — 1
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Hint 1 of 2
First get the rectangle's area, then the grey part is half of it.
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Hint 2 of 2
The grey piece is the part of the 6×6 square lying below line AB; its height is 6 − PX.
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Approach: set grey area equal to half the rectangle
- Rectangle ABCD is 10×6, area 60, so the grey part is 30.
- The square has side 6; the grey strip is 6 wide and (6 − PX) tall: 6(6 − PX) = 30.
- So 36 − 6·PX = 30, giving PX = 1.
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