A gardener has 91 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. If the length is to be twice its width, what will be the dimensions of the garden?

Let the width of the garden be \( x \) feet. According to the problem, the length of the garden is twice the width, so the length is \( 2x \) feet.

The border surrounding the garden is 2 feet wide, meaning the total width and length of the area enclosed by the fencing include an extra 4 feet (2 feet on each side). Thus, the dimensions of the total enclosed area are:
- Total width = \( x + 4 \) feet
- Total length = \( 2x + 4 \) feet

The total perimeter of the enclosed area (with the fencing) is given by:
\[
2 \times (\text{Total length} + \text{Total width}) = 91 \, \text{feet}
\]
Substituting the expressions for the total length and total width:
\[
2 \times ((2x + 4) + (x + 4)) = 91
\]
Simplify the equation:
\[
2 \times (3x + 8) = 91
\]
\[
6x + 16 = 91
\]
Solving for \( x \):
\[
6x = 91 - 16
\]
\[
6x = 75
\]
\[
x = \frac{75}{6} = 12.5 \, \text{feet}
\]

Thus, the width of the garden is \( 12.5 \) feet, and the length of the garden is:
\[
2x = 2 \times 12.5 = 25 \, \text{feet}
\]

### Final Dimensions of the Garden:
- Width = 12.5 feet
- Length = 25 feet

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. What would the dimensions be if the length was three times the width?
2. How would the problem change if the border was 3 feet wide instead of 2 feet?
3. What if the gardener had 100 feet of fencing instead of 91?
4. How would the problem change if the border only surrounded the length of the garden?
5. How much area is enclosed by the fencing, including the border?

**Tip:** When dealing with problems involving perimeters and borders, always account for the extra length added by the border to both dimensions.

Learn how to determine the dimensions of a garden enclosed by 91 feet of fencing with a 2-foot border, where the length is twice the width. This problem involves algebra and geometry, focusing on the perimeter of a rectangle and solving for dimensions. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation