To solve this, we need to calculate the sum of all the sides of the shape and ensure that it is less than 24.1 cm.

Given:
- Side 1 = 6.8 cm
- Side 2 = \( x \) cm (unknown)
- Side 3 = 7.9 cm
- Side 4 = 6.4 cm
- The perimeter should be less than 24.1 cm.

The perimeter of a shape is the sum of all its sides:

\[
P = 6.8 + x + 7.9 + 6.4
\]

According to the condition given:

\[
6.8 + x + 7.9 + 6.4 < 24.1
\]

Now let's solve for \( x \):

\[
21.1 + x < 24.1
\]

Subtract 21.1 from both sides:

\[
x < 24.1 - 21.1
\]

\[
x < 3
\]

So, \( x \) must be less than 3 cm.

Would you like further clarification, or have any questions?

Here are some related questions:
1. How does changing \( x \) affect the perimeter?
2. What happens if the perimeter exceeds 24.1 cm?
3. Can the perimeter ever be exactly 24.1 cm in this scenario?
4. What if the sides were in different units?
5. How would you calculate the area of the shape given the sides?

**Tip**: Always check the units when calculating perimeters, especially if dealing with mixed units!

Solve for the unknown side of a shape where the perimeter must be less than 24.1 cm. Learn key concepts in basic algebra and inequalities, and apply the perimeter formula. This step-by-step guide is ideal for students in Grades 6-8.

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