Problem 3 · 2012 Math Kangaroo
Easy
Number Theory
factor-pairs
How many different rectangles with area 60 and whole-numbered side lengths are there?
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Answer: B — 6
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Hint 1 of 2
A rectangle is fixed by a pair of side lengths whose product is 60.
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Hint 2 of 2
Count the unordered factor pairs of 60.
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Approach: count factor pairs of 60
- A rectangle with whole sides and area 60 corresponds to a factor pair of 60.
- The pairs are 1×60, 2×30, 3×20, 4×15, 5×12 and 6×10.
- That is 6 different rectangles.
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