A piece of tin is in the form of a rectangle having length 12 cm and width 8 cm. This is used to construct a closed cube. The side of the cube is:

The correct option is 4 cm.

Let's understand why this is the correct answer step-by-step.

Step 1: Understand the given material
We are given a rectangular piece of tin.
Length of the rectangle ($L$) = 12 cm
Width of the rectangle ($W$) = 8 cm

The area of this rectangular tin sheet is given by:
$\text{Area of rectangle}=L\times W$
$\text{Area of rectangle}=12 \mathrm{cm}\times 8 \mathrm{cm}=96 {\mathrm{cm}}^2$

Step 2: Understand the object to be constructed
This rectangular sheet is used to construct a closed cube.
Let the side length of the cube be $a$.
A closed cube has 6 identical square faces. The total surface area ($TSA$) of a closed cube of side $a$ is given by the formula:
$TSA=6a^2$

Step 3: Equate the areas
Since the entire sheet of tin is used to construct the cube, the total surface area of the cube must be equal to the area of the rectangular sheet:
$6a^2=96$

Step 4: Solve for the side of the cube ($a$)
Divide both sides of the equation by 6:
$a^2=\frac{96}{6}$
$a^2=16$

Taking the square root of both sides:
$a=\sqrt{16}$
$a=4 \mathrm{cm}$

Therefore, the side of the constructed cube is 4 cm.