https://file.aiquickdraw.com/mathbot/file/17287969410858ivhj080.jpg

The problem provided in the image can be translated as follows:

"Nabila is lifting a display shelf in the shape of a rectangle. If the width of the shelf is 4x and its length is 6x, and the perimeter of the rectangle is 1800, what is the value of x?"

We can solve this step by step.

### Step 1: Formula for the perimeter of a rectangle
The perimeter (P) of a rectangle is given by:
\[
P = 2 \times ( \text{length} + \text{width} )
\]
In this case, the length is \(6x\) and the width is \(4x\). So, the formula becomes:
\[
P = 2 \times (6x + 4x)
\]
\[
P = 2 \times 10x
\]
\[
P = 20x
\]

### Step 2: Set the perimeter equal to 1800
From the problem, we know the perimeter is 1800, so:
\[
20x = 1800
\]

### Step 3: Solve for \(x\)
Divide both sides by 20:
\[
x = \frac{1800}{20}
\]
\[
x = 90
\]

Thus, the value of \(x\) is 90.

Would you like a more detailed explanation, or do you have any further questions? 

Here are some related questions you might want to explore:
1. What is the length of the shelf if \(x = 90\)?
2. What is the width of the shelf if \(x = 90\)?
3. How do you derive the formula for the perimeter of a rectangle?
4. What would the perimeter be if the length and width were doubled?
5. How does changing the value of \(x\) affect the perimeter?

**Tip:** Always check if the units (if any) are consistent throughout a word problem for a more accurate solution.

Nabila is lifting a display shelf in the shape of a rectangle. If the width of the shelf is 4x and its length is 6x, and the perimeter of the rectangle is 1800, what is the value of x?

Find the value of x in a rectangle problem where the width is 4x, the length is 6x, and the perimeter is 1800. This solution walks you through the formula and step-by-step calculations. Perfect for Grades 7-9 geometry students.

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