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When sending a rectangular package through the U.S. Postal Service, the combined length and girth (perimeter of the cross section) cannot exceed 108 inches. Up to what length can a package be if the width and height are 10 and 15 inches?

Answer :

Let W = width of package
Let H = height of package
Let L = length of package

The perimeter cab be one of the following:
P = 2(L + W),  or
P = 2(L + H)

The perimeter of the cross section cannot exceed 108 in.
When the width is 10 in, then
 2(L + 10) <= 108
 L + 10 <= 54
 L <= 44 in

When the height is 15 in, then
2(L + 15) <= 108
L + 15 <= 54
L <= 39 in

To satisfy both of these conditions requires that L <= 39 in.

Answer: 39 inches

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