Problem 5 · 2009 Math Kangaroo
Easy
Geometry & Measurement
area-fraction
In the picture the large square has an area of 1. What is the area of the small black square?
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Answer: D — 1900
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Hint 1 of 2
Each zoom-in shrinks the side of the next square by a fixed factor.
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Hint 2 of 2
Track how many times the side shrinks, then square that ratio for the area.
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Approach: follow the repeated scaling of the side length
- The black square sits inside nested subdivisions of the unit square.
- Following the repeated shrinking down to the black cell, its side is 1/30 of the whole.
- Its area is therefore (1/30)^2 = 1/900 of the large square.
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