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:

$$
54 = 2 \ imes (L + W)
$$

$$
54 = 2 \ imes ((2W + 3) + W)
$$

Continue Reading

The altitude corresponding to side $a$ is $h_a = \frac{2A}{a} = \frac{168}{13} \approx 12.92$, for $b$ it is $h_b = \frac{168}{14} = 12$, and for $c$ it is $h_c = \frac{168}{15} = 11.2$. The shortest altitude corresponds to the longest side, which is $15$, yielding:
Question: A glaciologist models a cross-section of a glacier as a right triangle, where the hypotenuse represents the slope surface of length $z$, and the inscribed circle has radius $c$. If the ratio of the area of the circle to the area of the triangle is $\frac{\pi c^2}{\frac{1}{2}ab}$, express this ratio in terms of $z$ and $c$.
Solution: In a right triangle with legs $a$, $b$, and hypotenuse $z$, the inradius is given by:

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Final Thoughts

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: