When the diagram in Figure 2 is folded along the dashed lines the height of the box will be 3 inches. Hence the square removed from each corner is 3 × 3. It follows that we can label portions of the diagram as shown next.
It follows that 14 = W - 6 and 34 = L - 6. Hence the dimensions of the smallest rectangular piece of material that can be used to construct this box is W = 20 and L = 40.
A more general setting.
Consider a box of this type with volume V = xyz as shown in the next figure.
Determine equations for the length L and width W of the smallest rectangular piece of material that can be used to construct this box.
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