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4 Encuentra la medida del lado de cada figura si se sabe que el perímetro de cada una es 60 cm.

To solve this problem, we need to find the value of \( x \) given that the perimeter of the rectangle is 60 cm.

### Step 1: Express the Perimeter of the Rectangle
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times \text{length} + 2 \times \text{width}
\]
In this case, the length is \( 2x \) and the width is \( x \). Therefore, the formula for the perimeter becomes:
\[
P = 2 \times 2x + 2 \times x = 4x + 2x = 6x
\]

### Step 2: Set Up the Equation
We are given that the perimeter is 60 cm. Therefore, we can set up the equation:
\[
6x = 60
\]

### Step 3: Solve for \( x \)
To find \( x \), divide both sides of the equation by 6:
\[
x = \frac{60}{6} = 10 \text{ cm}
\]

So, the value of \( x \) is 10 cm.

### Conclusion
The dimensions of the rectangle are \( 2x = 20 \) cm for the length and \( x = 10 \) cm for the width.

Would you like more details or have any questions about the solution?

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Here are 5 related questions to expand your understanding:
1. What would be the area of the rectangle with the given dimensions?
2. If the width was increased by 5 cm, what would be the new perimeter?
3. How would the perimeter change if the length was doubled?
4. What would happen to the value of \( x \) if the perimeter was instead 90 cm?
5. If the length and width are multiplied by a factor of 2, what would be the new perimeter?

**Tip:** Understanding how to manipulate algebraic expressions is key in solving geometry problems involving perimeter and area.

Learn how to find the dimensions of a rectangle with a perimeter of 60 cm using algebraic equations. This problem explores the concept of perimeter in geometry and involves solving equations with one variable. Suitable for students in Grades 6-8.

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