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 ([tex]A_{s}[/tex]), measured in square centimeters, is defined by the following formula:
[tex]A_{s} = 2\cdot (w\cdot h + w\cdot l + h\cdot l)[/tex] (1)
Where:
[tex]w[/tex] - Width, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
[tex]l[/tex] - Length, measured in centimeters.
If we know that [tex]A_{s} = 7440\,cm^{2}[/tex], [tex]w = 40\,cm[/tex] and [tex]h = 36\,cm[/tex], then the length of the rectangular box is:
[tex]2880 +80\cdot l + 72\cdot l = 7440[/tex]
[tex]152\cdot l = 4560[/tex]
[tex]l = 30\,cm[/tex]
The length of the rectangular box is 30 centimeters.
