AMC 10 Step by Step
2015 AMC 10BProblem 25P21-25~8 minPrint

A rectangular box measures a×b×ca \times b \times c , where a,a, b,b, and cc are integers and 1abc1 \leq a \leq b \leq c . The volume and surface area of the box are numerically equal. How many ordered triples (a,b,c)(a,b,c) are possible?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.