Question

A rectangular box is 40 cm wide and 36 cm high. If the surface area of the box is 7440 square centimeters, find the length of the box.

Answer 1

The length of the rectangular box is 30 centimeters.

Explanation:

Let suppose that rectangular box is closed. The rectangular box is represented by a parallelepiped, whose surface area (
`A_(s)`), measured in square centimeters, is defined by the following formula:

`A_(s) = 2\cdot (w\cdot h + w\cdot l + h\cdot l)` (1)

Where:

`w` - Width, measured in centimeters.

`h` - Height, measured in centimeters.

`l` - Length, measured in centimeters.

If we know that
`A_(s) = 7440\,cm^(2)`,
`w = 40\,cm` and
`h = 36\,cm`, then the length of the rectangular box is:

`2880 +80\cdot l + 72\cdot l = 7440`

`152\cdot l = 4560`

`l = 30\,cm`

The length of the rectangular box is 30 centimeters.