The perimeter of a rectangle of 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.

To find the length and width of the rectangle, we can use the following information:

1. The perimeter of the rectangle is 150 feet.
2. The length (\(L\)) is twice the width (\(W\)).

### Step 1: Use the formula for the perimeter of a rectangle
The perimeter \(P\) of a rectangle is given by the formula:
\[
P = 2L + 2W
\]
We know that the perimeter \(P = 150\) feet, so we can write:
\[
150 = 2L + 2W
\]

### Step 2: Express the length in terms of the width
Since the length is twice the width, we can write:
\[
L = 2W
\]

### Step 3: Substitute \(L = 2W\) into the perimeter equation
Now substitute \(L = 2W\) into the perimeter equation:
\[
150 = 2(2W) + 2W
\]
Simplifying this equation:
\[
150 = 4W + 2W
\]
\[
150 = 6W
\]

### Step 4: Solve for the width \(W\)
To find the width, divide both sides of the equation by 6:
\[
W = \frac{150}{6} = 25 \, \text{feet}
\]

### Step 5: Find the length \(L\)
Now that we know the width is 25 feet, substitute this value into the equation \(L = 2W\):
\[
L = 2 \times 25 = 50 \, \text{feet}
\]

### Final Answer:
- **Width** = 25 feet
- **Length** = 50 feet

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would the perimeter change if the width were increased by 5 feet?
2. What would the area of this rectangle be?
3. If the width was halved, what would the new dimensions and perimeter be?
4. How would the solution change if the perimeter was 200 feet instead of 150 feet?
5. Can you derive a general formula for the width and length if the perimeter and the relationship between length and width are known?

**Tip:** When dealing with geometric problems, always check if relationships between sides can help simplify equations.

Learn how to solve for the length and width of a rectangle with a perimeter of 150 feet, where the length is twice the width. This problem covers key geometric concepts, including the perimeter formula and simple algebra. Suitable for students in Grades 5-7.

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