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?

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