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? - Treasure Valley Movers

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: