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The problem involves calculating the perimeter and area of a rectangular plot of land that Vicente is enlarging. Initially, the land is 20 feet by 30 feet, and Vicente is expanding its length by adding \(x\) feet to one side, as shown in the figure.

Let's break down how to find the polynomials for the perimeter and area of the enlarged plot.

1. **Area (A)**:
   The area of a rectangle is given by:
   \[
   A = \text{length} \times \text{width}
   \]
   Initially, the length is 30 feet, and the width is 20 feet. After the extension, the length becomes \(30 + x\) feet, while the width remains 20 feet. Therefore, the area is:
   \[
   A = (30 + x) \times 20 = 600 + 20x
   \]

2. **Perimeter (P)**:
   The perimeter of a rectangle is given by:
   \[
   P = 2 \times (\text{length} + \text{width})
   \]
   After the extension, the length is \(30 + x\) feet, and the width remains 20 feet. Thus, the perimeter becomes:
   \[
   P = 2 \times ((30 + x) + 20) = 2 \times (50 + x) = 100 + 2x
   \]

Based on these calculations, the correct choice is:
- \(P = 100 + 2x\) and \(A = 600 + 20x\).

This matches option **a** in the list of answers.

Let me know if you'd like further details or explanations.

Here are 5 related questions for practice:
1. How would the perimeter change if the width were also extended by \(y\) feet?
2. What happens to the area if \(x = 5\) feet?
3. How do you calculate the area of a triangle given the base and height?
4. If Vicente doubled the extension to \(2x\) feet, what would the new area be?
5. What is the perimeter of a square with side length \(s\)?

**Tip:** Always double-check your units and expressions when calculating areas and perimeters for enlarged shapes!

En la parte trasera de su finca, Vicente siembra verduras. El terreno mide 20 por 30 pies. Vicente decide agrandarlo (como muestra la figura). Dos polinomios en términos de x que representan el perímetro y el área del terreno agrandado respectivamente son: P = 100 + 2x y A = 600 + 20x

Resuelve un problema que involucra el perímetro y el área de un terreno rectangular que se agranda. Con polinomios representando el área y el perímetro en función de x, este problema cubre conceptos clave de álgebra y geometría.

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