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2015 AMC 10B Question 25

AMC10 · 2015 AMC 10B

Question 25

A rectangular box measures $a \times b \times c,$ where $a,$ $b,$ and $c$ are integers and $$
1\leq a \leq b \leq c.
$$ The volume and the surface area of the box are numerically equal. How many ordered triples $(a,b,c)$ are possible?
  1. $ 4 $
  2. $ 10 $
  3. $ 12 $
  4. $ 21 $
  5. $ 26 $