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The diagram represents the layout of a house, with the perimeter of the lot being given as 146 meters. The dimensions of various parts of the house are expressed in terms of the variable \(x\), and the task is to calculate the dimensions of the lot based on the given perimeter.

Let's break it down:

1. The total perimeter is 146 meters.
2. The perimeter of a rectangle is given by:
   \[
   \text{Perimeter} = 2(\text{Length} + \text{Width})
   \]

Based on the image:
- The length of the lot (horizontal sides) consists of several segments:
  \[
  (6x + 1) + (2x - 1) + (5x + 3)
  \]
- The width of the lot (vertical sides) consists of:
  \[
  (3x + 2) + (5x + 2)
  \]

Thus, the perimeter equation becomes:
\[
2 \left( [(6x + 1) + (2x - 1) + (5x + 3)] + [(3x + 2) + (5x + 2)] \right) = 146
\]

I will now simplify this and solve for \(x\).The value of \(x\) is \( \frac{22}{7} \), or approximately 3.14.

Substituting this back into the expressions for the length and width of the lot:
- The length of the lot is \( \frac{307}{7} \), which is approximately 43.86 meters.
- The width of the lot is \( \frac{204}{7} \), which is approximately 29.14 meters.

Thus, the dimensions of the lot are approximately **43.86 meters by 29.14 meters**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How can we verify the calculated perimeter?
2. What is the area of the lot based on these dimensions?
3. How would the dimensions change if the perimeter were different?
4. Can we determine the area of each room given the value of \(x\)?
5. How do we calculate the diagonal of the lot using the dimensions?

**Tip:** Always double-check your results by substituting back into the original formula to verify.

Calcule las dimensiones del terreno con un perímetro de 146 metros según el plano mostrado.

Learn how to calculate the dimensions of a lot with a perimeter of 146 meters based on algebraic expressions for the lengths and widths of a house's layout. This step-by-step guide covers essential concepts in algebra and geometry, perfect for high school students.

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