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Problem 347: (2015 AMC 10b, 25; 12b 23)
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? $\textbf{(A)}\; 4 \qquad$ $\textbf{(B)}\; 10 \qquad$ $\textbf{(C)}\; 12 \qquad$ $\textbf{(D)}\; 21 \qquad$ $\textbf{(E)}\; 26$
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Exercise 347: Solution
A rectangular box measures $a\times b\times c$, where $a$, $b$, and $c$ are integers and $1\le a\le b\le c$. The volume of the box is twice its surface area. How many ordered triples $(a,b,c)$ are possible?
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