A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter is 54 meters, what are the dimensions of the garden?
Rectangular Garden Dimensions: Solving for Length and Width with a 54-Meter Perimeter
Designing a rectangular garden isn’t just about aesthetics—it’s about getting precise measurements to make the most of your space. If you’re planning a garden where the length is 3 meters more than twice the width and the total perimeter is 54 meters, this SEO-friendly article explains how to calculate the exact dimensions using basic algebra and geometry.
Understanding the Relationship Between Length and Width
Let the width of the garden be represented by $ W $ (in meters). According to the problem, the length $ L $ is defined as:
$$L = 2W + 3$$
This relationship sets up a clear algebraic link between the two key dimensions of your rectangular garden.
Using the Perimeter Formula
The perimeter $ P $ of a rectangle is calculated with the formula:
$$P = 2 \ imes (\ ext{Length} + \ ext{Width})$$
Substituting the known perimeter (54 meters) and the expression for $ L $, we get:
$$54 = 2 \ imes (L + W)$$
$$54 = 2 \ imes ((2W + 3) + W)$$
Simplify the expression inside the parentheses:
$$54 = 2 \ imes (3W + 3)$$
$$54 = 6W + 6$$
Solving for Width $ W $
Subtract 6 from both sides:
$$48 = 6W$$
Divide by 6:
$$W = 8 \ ext{ meters}$$
Calculating the Length $ L $
Now substitute $ W = 8 $ into the length formula:
$$L = 2(8) + 3 = 16 + 3 = 19 \ ext{ meters}$$
Final Dimensions
- Width: 8 meters- Length: 19 meters
Verifying the perimeter:$$2 \ imes (19 + 8) = 2 \ imes 27 = 54 \ ext{ meters}$$✔️ The calculations match the given perimeter.
Why Knowing Garden Dimensions Matters
Knowing the exact size of your garden helps with efficient planting, irrigation planning, and space utilization. With a width of 8 meters and length of 19 meters, your rectangular garden offers ample growing area while fitting neatly into most backyard layouts.
Conclusion
A rectangular garden measuring 8 meters in width and 19 meters in length perfectly satisfies the condition that the length is 3 meters more than twice the width and yields a total perimeter of 54 meters. Whether you're a home gardener, landscaper, or DIY enthusiast, understanding how to calculate dimensions using real-world relationships empowers you to design beautiful, functional outdoor spaces.
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