Problem 11 · 2014 Math Kangaroo
Medium
Geometry & Measurement
area-decomposition
A cuboid-shaped box has the measurements \(a imes b imes c\) with \(a
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Answer: A — If one increases \(a\).
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Hint 1 of 2
Stretching one edge by 5 adds a slab whose volume is 5 times the product of the OTHER two edges.
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Hint 2 of 2
To make that slab biggest, you want the other two edges as large as possible.
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Approach: compare the slabs added by each stretch
- Increasing edge a by 5 adds 5·b·c; increasing b adds 5·a·c; increasing c adds 5·a·b.
- Since a < b < c, the largest of the products bc, ac, ab is bc.
- That biggest gain comes from stretching the SMALLEST edge a, so the answer is (A): increase a.
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