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The question asks to find the value of \( x \) that determines the exact dimensions of the rectangular area with dimensions \( (x + 2) \) meters by \( (x + 4) \) meters, and an area of 195 m².

### Steps to solve:

1. The area of a rectangle is calculated by multiplying the length and width. So, the equation is:
   \[
   (x + 2)(x + 4) = 195
   \]
   
2. Expanding the left-hand side:
   \[
   (x + 2)(x + 4) = x^2 + 4x + 2x + 8 = x^2 + 6x + 8
   \]
   
   Now the equation becomes:
   \[
   x^2 + 6x + 8 = 195
   \]
   
3. Subtract 195 from both sides to set the equation to 0:
   \[
   x^2 + 6x + 8 - 195 = 0
   \]
   \[
   x^2 + 6x - 187 = 0
   \]

4. Now, solve this quadratic equation using the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   Where \( a = 1 \), \( b = 6 \), and \( c = -187 \).

5. Substituting the values:
   \[
   x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-187)}}{2(1)}
   \]
   \[
   x = \frac{-6 \pm \sqrt{36 + 748}}{2}
   \]
   \[
   x = \frac{-6 \pm \sqrt{784}}{2}
   \]
   \[
   x = \frac{-6 \pm 28}{2}
   \]

6. Now calculate the two possible values for \( x \):
   \[
   x = \frac{-6 + 28}{2} = \frac{22}{2} = 11
   \]
   or
   \[
   x = \frac{-6 - 28}{2} = \frac{-34}{2} = -17
   \]

Since \( x \) represents a dimension, it must be positive. Therefore, \( x = 11 \).

### Answer: \( x = 11 \), corresponding to option **c)**.

Would you like more details or have any further questions?

Here are some related questions:
1. How do you expand binomials in algebra?
2. What is the quadratic formula, and when is it used?
3. Can you solve quadratic equations by factoring instead of using the formula?
4. How do you verify if a solution to a quadratic equation is correct?
5. What are real-life applications of solving quadratic equations?

**Tip:** When solving a quadratic equation, always check if it can be factored easily before using the quadratic formula, as factoring can save time.

No próximo mês, a prefeitura irá fazer a revitalização de uma praça e precisa saber exatamente as dimensões para preparar o terreno e plantar a grama. Sabendo que as dimensões do terreno são x + 2 de largura e x + 4 de comprimento, o valor de x que determina as dimensões exatas da praça é?

Find the dimensions of a rectangular area by solving a quadratic equation. This problem involves algebraic concepts such as quadratic equations and the formula for the area of a rectangle. Suitable for students in Grades 8-10.

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