Problem 254 - Elementary Algebra

Question

In the following exercises, solve using rectangle properties. A driveway is in the shape of a rectangle 20 feet wide by 35 feet long. What is its perimeter?

Step-by-Step Solution

Answer

The perimeter is 110 feet.

Step 1: Identify the Formula for Perimeter

The perimeter of a rectangle is calculated using the formula: \[ P = 2L + 2W \] where \( L \) is the length and \( W \) is the width.

Step 2: Substitute the Given Values

In this problem, the length \( L \) is 35 feet and the width \( W \) is 20 feet. Substitute these values into the formula: \[ P = 2(35) + 2(20) \]

Step 3: Perform the Multiplications

First, multiply 2 by 35: \[ 2(35) = 70 \] Next, multiply 2 by 20: \[ 2(20) = 40 \]

Step 4: Add the Results

Finally, add the two results from the previous step: \[ P = 70 + 40 \] This yields: \[ P = 110 \]

Key Concepts

Perimeter Formula

Understanding the perimeter formula is key to solving many geometry problems.
The perimeter of a rectangle is the total distance around its edges.
Mathematically, it is expressed as: \[ P = 2L + 2W \] where `P` represents the perimeter, `L` is the length, and `W` is the width.
This formula works because a rectangle has two pairs of opposite sides that are equal and parallel.
Thus, the combined lengths of all sides are calculated by doubling the length and width before adding them together.
Knowing this formula helps to solve any problem involving the perimeter of a rectangle.

Rectangle Dimensions

Knowing how to identify a rectangle's dimensions is essential.
The length is usually the longer side, and it is denoted by `L` in the formula.
The width is the shorter side, which is denoted by `W`.
In this exercise, the driveway's length is given as 35 feet, and the width is 20 feet.
Always carefully observe the problem statement to correctly assign length and width values.
Misidentifying dimensions could lead to incorrect calculations and results.

Geometry Problem-Solving

Solving geometry problems involves a systematic approach.
This exercise demonstrated a clear, step-by-step method to find the perimeter.
First, identify the applicable formula; in this case, the perimeter formula for a rectangle.
Next, substitute the known values into the formula.
It's crucial to follow the correct sequence of mathematical operations.
For instance, perform the multiplications before the addition.
This logical sequence helps ensure that the calculations are accurate and complete.

Elementary Algebra Exercises

Elementary algebra is fundamental in geometry problem-solving.
In this exercise, simple algebraic principles were applied: identifying variables, substituting values, and performing arithmetic.
The exercise relied on the variable substitution method and basic operations like multiplication and addition.
Practicing elementary algebra in geometry exercises helps solidify one's understanding and application of these concepts.
This foundational algebraic skill is important and widely applicable in various math problems.