Problem 9 · 2015 Math Kangaroo
Easy
Geometry & Measurement
area-fractionfolding
One corner of a square piece of paper is folded into the middle of the square. That way an irregular pentagon is created. The numerical values of the areas of the pentagon and the square are consecutive whole numbers. What is the area of the square?
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Answer: C — 8
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Hint 1 of 2
Folding one corner to the centre removes a triangle, so the pentagon area is the square area minus that triangle.
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Hint 2 of 2
Write the square area as A; the removed triangle is A/8, so the pentagon is 7A/8, and the two areas are consecutive whole numbers.
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Approach: express the removed triangle as a fraction of the square
- Folding a corner into the centre covers a triangle equal to one eighth of the square.
- So the pentagon has area A - A/8 = 7A/8, where A is the square area.
- Square and pentagon are consecutive whole numbers, so their difference A/8 = 1, giving A = 8.
- So the area of the square is 8 (C).
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