Question

United Parcel Service (UPS) will only ship packages for which the length is less than or equal to 108 inches and the length plus the girth is less than or equal to 130 inches. The length of a package is defined as the length of the longest side. The girth is defined as twice the width plus twice the height of the package. If a box has a length of 34 inches and a width of 22 inches, determine the possible range of heights h for this package if you wish to ship it by UPS. (Source: .)

Answer 1

To ship a package via UPS with a length of 34 inches and a width of 22 inches, the height must be less than or equal to 31 inches, as UPS's size requirement states the length plus the girth (twice the width plus twice the height) must not exceed 130 inches.

Step-by-step explanation:

The United Parcel Service (UPS) has specific size requirements for the packages it will ship. UPS requires that the length of the package (the longest side) be less than or equal to 108 inches, and the combined length and girth must be less than or equal to 130 inches. The girth is calculated by adding together twice the width and twice the height of the package. To determine the possible heights for a package with a length of 34 inches and a width of 22 inches that can be shipped via UPS, we can use the formula:

L + 2W + 2H ≤ 130 inches (where L is length, W is width, and H is height).

Plug in the known values:

34 + 2(22) + 2H ≤ 130

68 + 2H ≤ 130

2H ≤ 62

H ≤ 31 inches

The possible range of heights h for the package is 0 inches to 31 inches.