SOLUTION: Grace constructed an open box with a square base out of 192 square centimeters material. The height of the box is 4 centimeter. What is the length of the side of the base of the bo

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Question 885188: Grace constructed an open box with a square base out of 192 square centimeters material. The height of the box is 4 centimeter. What is the length of the side of the base of the box?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of each side of the square base of the box, in centimeters.
x%5E2= surface area of the base of the box, in square centimeters.
4x= length of the perimeter of the square base of the box, in centimeters.
%284x%29%2A4=16x= lateral surface area of the box (all four sides), in square centimeters.
x%5E2%2B16x=192= total surface area of the box (base plus all four sides), in square centimeters.

x%5E2%2B16x=192
x%5E2%2B16x%2B64=192%2B64
%28x%2B8%29%5E2=256
%28x%2B8%29%5E2=16%5E2
The solutions to that equation come from
x%2B8=16--->x=16-8--->highlight%28x=8%29
and from x%2B8=-16--->x=-16-8--->x=-24 .
Since x is the length of a side of the base (in centimeters),
and is expected to be a positive number,
the length of each side of the square base of that box is
highlight%288%29 centimeters.