https://r2.erweima.ai/mathbot/image/17255013775344z8a8knm.jpg

The image contains two rectangular shapes, each with their respective perimeter values and some dimensions provided. The task is to calculate the value of the missing side denoted as "x" and the length of the other sides based on the given perimeters.

### Observations:
1. **Figure A**:
   - Perimeter: 32 cm
   - One side: 8 cm (given)
   - The other side: unknown (denoted as \( x \))

2. **Figure B**:
   - Perimeter: 32 cm
   - One side: 10 cm (given)
   - The other side: 12 cm (given)

### Step-by-Step Solutions:

#### **For Figure A**:
The formula for the perimeter of a rectangle is:
\[
P = 2 \times (L + W)
\]
Where:
- \( P \) is the perimeter
- \( L \) is the length
- \( W \) is the width

Given that the perimeter is 32 cm, and one side is 8 cm, let \( x \) be the unknown side:
\[
32 = 2 \times (8 + x)
\]
Simplifying the equation:
\[
32 = 16 + 2x
\]
\[
2x = 32 - 16 = 16
\]
\[
x = \frac{16}{2} = 8 \, \text{cm}
\]
So, the missing side in Figure A is \( x = 8 \, \text{cm} \).

#### **For Figure B**:
In this case, both dimensions (10 cm and 12 cm) are provided, and the perimeter is given as 32 cm. Let's check if the given dimensions are consistent with the perimeter formula:
\[
P = 2 \times (10 + 12)
\]
\[
P = 2 \times 22 = 44 \, \text{cm}
\]
However, the perimeter is listed as 32 cm in the problem, which suggests there may be a mistake in either the given perimeter or dimensions.

Would you like me to clarify or check anything further, or go into more detail?

### Additional Questions:
1. How does the perimeter formula apply when only one dimension is given?
2. What happens if both sides of a rectangle are equal in length?
3. How would the area of these rectangles be calculated?
4. What if the perimeter changes, but the side lengths stay the same?
5. How can you confirm if a mistake is made in a geometry problem like this?

### Tip:
Always double-check the dimensions and given formulas to ensure they match before solving!

ACTIVIDAD 10: Calcular el valor de la incógnita 'x' y la longitud de los lados desconocidos. Figura A tiene un perímetro de 32 cm con un lado de 8 cm, y Figura B tiene un perímetro de 32 cm con lados de 10 cm y 12 cm.

Learn how to find the missing side lengths in rectangular figures with a given perimeter. In this example, a rectangle with a perimeter of 32 cm has one side of 8 cm (Figure A), and another with sides of 10 cm and 12 cm (Figure B). Suitable for Grades 5-6 geometry practice.

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