Emily is designing a garden with a rectangular layout. The length of the garden is 5 meters longer than twice its width. If the perimeter of the garden is 54 meters, what are the dimensions of the garden? - Coaching Toolbox
Title: Designing a Perfect Rectangular Garden: Dimensions Revealed
Title: Designing a Perfect Rectangular Garden: Dimensions Revealed
Creating a beautiful, functional garden begins with thoughtful planning—especially when it comes to layout and measurement. In this detailed example, we explore how to determine the exact dimensions of a rectangular garden where the length is tied to the width in a specific mathematical relationship. For garden designers and DIY enthusiasts alike, understanding these constraints helps maximize space and aesthetics.
When designing a rectangular garden, every dimension plays a critical role. In this case, Emily has crafted her garden with a creative approach: the length (L) is 5 meters longer than twice the width (W). This relationship can be expressed with the equation:
L = 2W + 5
Understanding the Context
What makes this design even more precise is the garden’s perimeter, a key factor in planning material use, plants placement, and overall structure. Emily’s garden has a total perimeter of 54 meters. The formula for the perimeter (P) of a rectangle is:
P = 2(L + W)
Substituting the known perimeter into the equation:
54 = 2(L + W)
Dividing both sides by 2 simplifies the equation:
27 = L + W
Now, substitute Emily’s expression for L into this equation:
27 = (2W + 5) + W
27 = 3W + 5
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Key Insights
Subtract 5 from both sides:
22 = 3W
Divide by 3:
W = 22/3 ≈ 7.33 meters (or 7 meters and 1 inch)
Now that we have the width, we can find the length using the earlier equation:
L = 2W + 5 = 2(22/3) + 5 = 44/3 + 15/3 = 59/3 ≈ 19.67 meters (or 19 meters and 8 inches)
Summary of Garden Dimensions:
- Width: 7.33 meters (±7 m 1 in)
- Length: 19.67 meters (±19 m 8 in)
- Perimeter: 54 meters (confirmed)
- Shape: Rectangular, optimized for efficient space utilization
This precise design showcases how combining algebraic relationships with real-world measurements leads to well-planned garden layouts. For gardeners, architects, and landscape designers, Emmily’s method—defining width, linking length mathematically, and solving systematically—provides a clear path to creative and accurate garden planning.
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Whether you’re starting a small backyard plot or a larger landscape project, understanding dimensions through equations empowers you to visualize, plan, and build with confidence. For Emily, this structured approach not only meets the 54-meter perimeter goal but also creates a balanced and inviting outdoor space.
If you’re designing your own garden, remember: a solid foundation begins with clear measurements—and sometimes, a little math goes a long way.
