Solution:

The question states that the equilateral triangle and the square have the same perimeter. The side length of the triangle is given as 10.4 cm. Let's calculate the side length of the square step by step.

Step 1: Perimeter of the equilateral triangle

An equilateral triangle has three equal sides. Therefore, the perimeter $P$ of the triangle is given by:

$P = 3 \times \text{side length of the triangle}$

$P = 3 \times 10.4 = 31.2 \, \text{cm}$

Step 2: Perimeter of the square

The square also has the same perimeter as the triangle. Let the side length of the square be $s$. The perimeter of the square is given by:

$P = 4 \times s$

Since the perimeters are equal, we set the two equal:

$4 \times s = 31.2$

Step 3: Solve for $s$

Divide both sides of the equation by 4:

$s = \frac{31.2}{4} = 7.8 \, \text{cm}$

Final Answer:

The side length of the square is:

$\boxed{7.8 \, \text{cm}}$

Would you like a detailed explanation of any step?

Here are 5 related questions for practice:

1. If an equilateral triangle has a side length of 12 cm, what would be the side length of a square with the same perimeter?
2. A square has a perimeter of 40 cm. What is the length of each side?
3. How do you calculate the perimeter of a regular hexagon if the side length is given?
4. What is the formula for the area of a square, and how does it relate to the perimeter?
5. If the side length of a square is doubled, how does the perimeter change?

Tip: Always double-check the relationship between perimeter and side length in regular shapes!