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

The lateral area is expressed as the product of the perimeter of the base and the height. While the surface area is the sum of all areas. The lateral area and the surface area of the box is calculated as follows:

LA = Ph 
P = 2l + 2w = (2 x 17) + (2 x 5) = 44 cm
LA = 44 cm x 3.12 cm = 137.28 cm

SA = 2(lw + wh + lh)
SA = 2[(17x5) + (5x3.12) + (17x3.12)]
SA = 307.28 cm

Thus, the lateral area and the surface area are 137 cm and 307 cm, respectively.