Answer:
Length of the final sides: 6 cm and 16 cm
Explanation:
The lengths of the sides of the original box are

Later, a piece of tin is cut out from each corner; the piece cut out has the shape of the square: we can call the length of its generic side x. Therefore, the dimensions of the box will now be:

We also know that the area is

And the area can be written as product of length and width, therefore:

So we find:

Solving for x,

Which has two solutions:
x = 13 cm (this is larger than the initial length of the width, therefore we discard it)
x = 2 cm
So, the length of the new sides are
