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If the perimeter of a parallelogram is 600 meters and one side is represented as [tex]2x[/tex], what is the value of [tex]x[/tex]?

A. 50 meters
B. 100 meters
C. 200 meters
D. 150 meters

Answer :

Certainly! Let's go through finding the value of [tex]\( x \)[/tex] step-by-step.

1. Understand the components of the problem:
- We have a parallelogram with a total perimeter of 600 meters.
- One side of the parallelogram is represented as [tex]\( 2x \)[/tex].

2. Identify the formula for the perimeter of a parallelogram:
- The perimeter [tex]\( P \)[/tex] of a parallelogram is given by the formula:
[tex]\[
P = 2(\text{length} + \text{width})
\][/tex]
- In this case, if one side (let's call it the "length") is [tex]\( 2x \)[/tex], the opposite side (also the "length") is the same, [tex]\( 2x \)[/tex]. This represents two of the sides.

3. Setting up the equation:
- Based on our understanding, the problem simplifies similarly to using all four sides as [tex]\( 2x \)[/tex] each when all sides are represented uniformly, although typically it's not a standard setup for a parallelogram.
- Simplified interpretation: Perimeter can be computed as the sum of all sides:
[tex]\[
4 \times 2x = 600
\][/tex]

4. Solving for [tex]\( x \)[/tex]:
- Rearrange the equation:
[tex]\[
8x = 600
\][/tex]
- Divide both sides by 8 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{600}{8}
\][/tex]
[tex]\[
x = 75
\][/tex]

Therefore, the value of [tex]\( x \)[/tex] is 75 meters.

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