A garden is to contain 200ft if its length is to be twice the width p, what should its dimension be?

To solve this problem, let's denote the width of the garden as \( p \) feet. The length of the garden, according to the problem, is twice the width, so the length would be \( 2p \) feet.

The perimeter of a rectangle (which is the shape of the garden) is given by the formula:
\[
\text{Perimeter} = 2(\text{Length} + \text{Width})
\]

Given that the perimeter is 200 feet, we can write the equation as:
\[
200 = 2(2p + p)
\]

Now, let's solve for \( p \):

1. Simplify the equation:
\[
200 = 2(3p)
\]
\[
200 = 6p
\]

2. Divide both sides by 6 to solve for \( p \):
\[
p = \frac{200}{6} = 33.\overline{3} \text{ feet}
\]

So, the width \( p \) is approximately \( 33.33 \) feet. Since the length is twice the width, the length will be:
\[
2p = 2 \times 33.\overline{3} = 66.\overline{6} \text{ feet}
\]

### Dimensions of the Garden:
- **Width**: \( 33.\overline{3} \) feet
- **Length**: \( 66.\overline{6} \) feet

Would you like more details or have any questions?

### Related Questions:
1. How would the dimensions change if the perimeter was increased to 300 feet?
2. What would the area of the garden be with the given dimensions?
3. How would the equation change if the length was three times the width?
4. What would the width be if the length was fixed at 50 feet?
5. How can you convert the dimensions to meters?

### Tip:
When dealing with perimeter problems, always start by identifying the relationship between length and width before setting up the equation.

Learn how to calculate the dimensions of a garden given its perimeter and length-to-width ratio. Solve for the width and length using the perimeter formula and the relationship between length and width. Suitable for students in Grades 7-9.

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