Problem 57 - Prealgebra

Question

This stamp shows the Mexican artist Frida Kahlo. The stamp was issued in 2001 and is the first U.S. stamp to honor a Hispanic woman. The image area of the stamp has a width of 0.84 inches and a length of 1.41 inches. Find the perimeter of the image. (IMAGE CAN'T COPY)

Step-by-Step Solution

Answer

The perimeter of the image is 4.5 inches.

Step 1: Identify the Formula

To find the perimeter of a rectangle, you use the formula \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width of the rectangle.

Step 2: Substitute the Values

Insert the given values of the width and length into the formula. Here, the width \( w = 0.84 \) inches and the length \( l = 1.41 \) inches.

Step 3: Calculate the Perimeter

Using the formula: \( P = 2(1.41 + 0.84) \). First, calculate the sum inside the parenthesis: \( 1.41 + 0.84 = 2.25 \).

Step 4: Complete the Calculation

Multiply the sum by 2: \( 2 \times 2.25 = 4.5 \). The perimeter of the stamp's image is 4.5 inches.

Key Concepts

Understanding Geometry Formulas

Geometry formulas help us describe and quantify various features and dimensions of shapes. All basic shapes have specific attributes like length, width, perimeter, and area. For rectangles, we often need to find the perimeter or area depending on the context of the problem. The perimeter is the total distance around a shape. For a rectangle, this is done using the formula \( P = 2(l + w) \), where \( l \) represents the length, and \( w \) represents the width.

If we think about why it’s \( 2(l + w) \), we can visualize it as measuring each side along the length and the width, twice—once for each of the opposite sides of the rectangle. Understanding this formula allows you to quickly calculate the perimeter of any rectangular shape when the length and width are known.

• Useful for real-life applications, such as framing a picture or fencing a yard.
• Can be adapted for squares where the formula simplifies to \( P = 4l \).

The Role of Basic Arithmetic Operations

Basic arithmetic operations are crucial when working with geometry problems. These operations include addition, multiplication, and sometimes subtraction and division. In the problem of finding the perimeter of a rectangle, addition and multiplication are key.

First, you add the length and width. This step combines the two pairs of opposite sides of the rectangle. In our example, we added \( 1.41 + 0.84 = 2.25 \). Once you have the sum, you multiply by 2, since the perimeter involves two lengths and two widths. Thus, \( 2 \times 2.25 = 4.5 \).

• Addition helps in summing lengths or widths appropriately.
• Multiplication applies to replicate the sum of measurements around the shape.

Understanding these operations helps in performing accurate calculations, ensuring you know how to manipulate numbers correctly to reach a solution.

Real-World Applications of Perimeter Calculation

Calculating the perimeter has multiple real-world applications. It is not only useful in academic exercises but also in everyday situations. Consider planning garden landscapes—knowing the perimeter of different areas helps in estimating materials needed for borders or fences.

In the case of stamps or pictures, like the Frida Kahlo stamp, understanding its perimeter can be crucial for display or framing purposes. Collectors or designers might use this data to choose mats or frames that fit precisely around the object.

• For architects, the perimeter aids in creating detailed building plans.
• Crafters use it to design layouts for patterns or pieces.
• helps determine the amount of materials needed for projects involving tiling or construction.

Having a grip on these calculations enables efficient planning and budgeting, reflecting how math skills translate into practical advantages.