The length of a side of a rectangle is 6 cm. Find the length of another side if the perimeter of the rectangle is shorter than the perimeter of a square with a side of 4 cm.

To solve this problem, let's first determine the perimeter of the square with a side of 4 cm.

The perimeter \( P \) of a square is given by the formula:

\[
P = 4 \times \text{side}
\]

So for a square with a side of 4 cm:

\[
P = 4 \times 4 = 16 \text{ cm}
\]

Next, the perimeter of a rectangle is given by the formula:

\[
P = 2 \times (\text{length} + \text{width})
\]

Given that one side (length) of the rectangle is 6 cm, we can express the perimeter as:

\[
P = 2 \times (6 + \text{width})
\]

We need the perimeter of the rectangle to be shorter than 16 cm:

\[
2 \times (6 + \text{width}) < 16
\]

Dividing both sides by 2:

\[
6 + \text{width} < 8
\]

Subtracting 6 from both sides:

\[
\text{width} < 2
\]

Thus, the length of the other side (width) must be less than 2 cm. 

To summarize, the width of the rectangle can be any value less than 2 cm.

### Do you have any questions or need further details? 

Here are five related questions for further exploration:
1. How would the perimeter change if the width were exactly 2 cm?
2. What would happen to the area of the rectangle if the width is maximized to just below 2 cm?
3. How do you calculate the area of the rectangle given the dimensions?
4. What are the properties of rectangles and squares related to perimeter and area?
5. How can you graphically represent the relationship between the length and width of a rectangle? 

**Tip:** Always check the conditions given in a problem carefully to ensure all constraints are met.

The length of a side of a rectangle is 6 cm. Find the length of another side if the perimeter of the rectangle is shorter than the perimeter of a square with a side of 4 cm.

Explore how to find the width of a rectangle when one side is 6 cm and the perimeter must be less than that of a square with a side of 4 cm. This problem involves calculating perimeters and solving inequalities, suitable for Grades 6-8.

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