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

Answer:

The length of the rectangular box is 30 centimeters.

Step-by-step 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.