https://file.aiquickdraw.com/mathbot/file/1729541872240c2xqytqm.jpg

The problem describes a rectangular park with its dimensions expressed as follows:

- The shorter side (width) is \( 2x - 10 \) units.
- The longer side (length) is \( 4x - 140 \) units.

To find the **perimeter** of the rectangle, we use the formula for the perimeter of a rectangle:

\[
\text{Perimeter} = 2(\text{Length} + \text{Width})
\]

Substituting the given expressions:

\[
\text{Perimeter} = 2((2x - 10) + (4x - 140))
\]

First, simplify the expression inside the parentheses:

\[
(2x - 10) + (4x - 140) = 6x - 150
\]

Now, multiply by 2:

\[
\text{Perimeter} = 2(6x - 150) = 12x - 300
\]

Next, to find the value of the perimeter, we need to solve for \( x \). Since the perimeter options are given in terms of specific units (65, 120, 185, or 370 units), we can equate the simplified perimeter formula to each of the possible answers to determine the value of \( x \).

We can check if the perimeter is **120 units**:

\[
12x - 300 = 120
\]

Solving for \( x \):

\[
12x = 120 + 300
\]
\[
12x = 420
\]
\[
x = \frac{420}{12} = 35
\]

Now that \( x = 35 \), we can substitute this value back into the expressions for the length and width to verify:

\[
\text{Width} = 2(35) - 10 = 70 - 10 = 60 \, \text{units}
\]
\[
\text{Length} = 4(35) - 140 = 140 - 140 = 0 \, \text{units}
\]

Thus, the perimeter of the park is **120 units**. Therefore, the correct answer is **B. 120 units**.

Would you like further details or have any questions?

Here are 5 related questions to expand on the topic:
1. What is the area of the park given the same dimensions?
2. How would the perimeter change if both dimensions were doubled?
3. What is the length of the diagonal of the park using the Pythagorean theorem?
4. How would the perimeter formula change for a different shape, like a triangle?
5. How does changing only one side of the rectangle affect the perimeter?

**Tip:** When working with rectangles, always ensure to correctly identify which sides are being summed when calculating the perimeter.

The neighborhood park has a rectangular shape with dimensions expressed as: width = 2x - 10 and length = 4x - 140. What is the perimeter of the park?

Learn how to find the perimeter of a rectangular park with dimensions given as algebraic expressions. This problem involves using the perimeter formula for a rectangle and solving algebraic expressions. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation