#### 1351. A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 64 meters, what is the area of the garden? - AIKO, infinite ways to autonomy.

Understanding the Context

Why the Garden Perimeter Question Matters Right Now

The configuration of gardens—especially rectangular spaces—is increasingly central to sustainable living and outdoor lifestyle planning in the US. From urban balconies to suburban lawns, people are rethinking how square footage affects plant growth, irrigation scale, and maintenance effort. To make informed decisions, users naturally turn to practical calculations like perimeter and area. This problem isn’t just academic; it speaks to broader priorities like maximizing usable space, estimating materials, and aligning design with financial goals. In current trends, this balances creativity with calculative confidence—a key shift in how home spaces are managed.

The setup—length thrice the width, total perimeter 64 meters—mirrors real-world scenarios where homeowners convert rough blueprints into concrete measurements. Understanding how these dimensions interact empowers smarter choices, whether scaling a balcony planter, designing raised beds, or planting efficient flowerbeds.

How #### 1351. A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 64 meters, what is the area of the garden? Actually Works

Key Insights

This problem solves neatly using basic perimeter formulas. For any rectangle, perimeter equals twice the sum of length and width:
Perimeter = 2 × (length + width)

Given the relationship:
Let width = w, then length = 3w

Substitute into the formula:
64 = 2 × (3w + w)
64 = 2 × 4w
64 = 8w
w = 8 meters

Now find the length:
Length = 3 × 8 = 24 meters

Calculate area using the formula:
Area = length × width = 24 × 8 = 192 square meters

Final Thoughts

So, a rectangular garden with a perimeter of 64 meters, where length is three times the width, covers exactly 192 square meters of usable space.

Common Questions About This Garden Calculation

Q: Why not use guesswork—can this be calculated visually?
A: While visual estimation is helpful, precise dimensions ensure accurate material estimates—critical for budgeting and installation.

Q: Does changing the perimeter affect the ratio?
A: Yes; altering the perimeter changes total size, but the proportional relationship (length 3× width) stays consistent with the formula.

Q: Can I apply this to smaller or irregular garden beds?
A: Absolutely. This method establishes a foundation for scaling any rectangular space by defining width as a variable.

Opportunities and Realistic Considerations