A problem from the British Columbia Colleges Senior High School Contest for 2000:
If I place a 6 cm × 6 cm square on a triangle, I can cover up to 60% of the triangle. If I place the triangle on the square, I can cover up to 2/3 of the square. What is the area, in cm2, of the triangle?
(a) 22 4/5
(b) 24
(c) 36
(d) 40
(e) 60
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The answer is (d). The key is to see that these measures are one and the same: The triangle overlaps the square by the same amount that the square “underlaps” the triangle, so these areas are maximized at the same moment. If A is the area of the triangle, then 0.6A = 2/3 × 36, and A = 40 cm2.
From “The Skoliad Corner,” Crux Mathematicorum, December 2000.
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