Problem 252 - Elementary Algebra

Question

In the following exercises, solve using rectangle properties. The length of a rectangle is 26 inches and the width is 58 inches. What is the perimeter?

Step-by-Step Solution

Answer

The perimeter of the rectangle is 168 inches.

Step 1: Identify the formula for the perimeter

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

Step 2: Insert given values into the formula

Substitute the given length (26 inches) and width (58 inches) into the formula: \[ P = 2(26 + 58) \]

Step 3: Perform the operations inside the parentheses

First, add the length and width: \[ 26 + 58 = 84 \]

Step 4: Multiply by 2

Now, multiply the sum by 2 to find the perimeter: \[ P = 2 \times 84 = 168 \]

Step 5: Conclusion

The perimeter of the rectangle is 168 inches.

Key Concepts

Perimeter Formula

The perimeter of a rectangle is the total length of all its sides. To find it, we use a specific formula: \( P = 2 ( \text{length} + \text{width} ) \). This formula works because a rectangle has two lengths and two widths. By adding the length and width and then doubling that sum, we cover all sides of the rectangle.

For example, if the length of a rectangle is 26 inches and the width is 58 inches, you substitute these values into the formula: \( P = 2 (26 + 58) \). After simplifying, you get the perimeter.

Understanding the formula helps in solving various geometry problems, and it's a basic concept in math that you will use often.

Geometry

Geometry is all about shapes, sizes, and the properties of space. Rectangles are basic geometric shapes with four right angles and opposite sides that are equal in length.

When solving problems related to rectangles, knowing key properties simplifies the process. For instance:

• Opposite sides are equal in length.
• The angles are always 90 degrees.
• The perimeter is the sum of all side lengths.

Understanding these properties helps you apply the relevant formulas correctly and visualize the shape you are working with. It makes calculations much easier and accurate.

Basic Algebra Operations

Algebra is like a toolset in math. It involves working with numbers and symbols to solve equations. In the perimeter formula \( P = 2 ( \text{length} + \text{width} ) \), you use basic algebra operations like addition and multiplication.

Here’s how the operations work in the context of our example:

• First, you add the length and width (26 + 58). This step uses basic addition.
• Next, you multiply the result by 2 to get the perimeter. This step uses basic multiplication.

Mastering these operations is essential because they form the basis of more complex math problems. Practicing with simple formulas helps solidify your understanding and application of algebra in various scenarios.