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? - Parker Core Knowledge
Rectangular Garden Dimensions: Solving for Length and Width with a 54-Meter Perimeter
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
Understanding the Context
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
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Key Insights
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:
$$
54 = 2 \ imes (L + W)
$$
$$
54 = 2 \ imes ((2W + 3) + W)
$$
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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:
