The dimensions of the box are
It always helps to draw a diagram.
Originally, the box had dimensions
If we were to fold the red areas up to form the sides of the box, the box would have height
But the problem says the volume is
Now we have this system:
Plugging this in for
We know that
Note that these are the dimensions on the original metal sheet. When we take out the
When you check the dimensions of
Now let the length of the box be a cm and its width be b cm.
To keep the volume and height of the box at given value its base area
To construct the box 4 squares of dimension
Now let us see what happens if we try to find out a and b using equation (1) and (2).
Combining (1) and (2) we get
Now trying to find out
This shows that real solution is not possible with sheet area 1200cm^2.
But a real solution is possible with a minimum value of the perimeter of the base of the box i.e.
for real values of a and b,
Then by relation (2)
Now with this sheet area of
And the the dimension of the box then will be