What rectangular boxes, with integer sides, have their surface areas equal to their volumes? One example is $4$ by $6$ by $12$.
How to do this? No doubt different people will suggest different methods. Suppose the dimensions of the box are $a$, $b$ and $c$ units where $a \leq b \leq c$ . You might like to show that the problem amounts to solving the equation$1 = 2/a + 2/ b + 2/c$ and then show $3 \leq a\leq 6 , 3 \leq b \leq 12 , 3 \leq c \leq 144$.