An open box is made from a 20 cm x 3 cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 96 cm². What is the length of the sides of the squares.

Length of the final sides: 6 cm and 16 cm

Step-by-step 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

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