Problem 47 - Algebra 1

Question

MULTIPLE CHOICE A rectangular computer screen measures 28 centimeters by 21 centimeters. What is the perimeter of the screen? A \(49 \mathrm{cm}\) B \(98 \mathrm{cm}\) C \(294 \mathrm{cm}\) D) \(588 \mathrm{cm}\)

Step-by-Step Solution

Answer

The perimeter of the screen is 98 centimeters. So, the correct answer is B, 98 centimeters.

Step 1: Understanding the Perimeter of a Rectangle Formula

The formula for getting the perimeter of a rectangle is \(2 \times (length + width)\). This means multiplying the sum of the length and width of the rectangle by 2.

Step 2: Substitute the Values into the Formula

The length of the rectangle is 28 centimeters and the width is 21 centimeters. Substituting these values into the formula gives \(2 \times (28 + 21)\).

Step 3: Calculate the Sum and Multiply by 2

First, find the sum of 28 and 21, which is 49. Then multiply this by 2 to get the perimeter of the rectangle. \(2 \times 49\) equals 98.

Key Concepts

Rectangle

A rectangle is a common geometric shape characterized by having four sides and four right angles. Its opposite sides are parallel and of equal length. Rectangles are used in various real-life applications and layouts, making them essential to understand in mathematics.

• Opposite sides are equal: This means if one side is given a certain length, its opposing side will have the same measurement.
• Right angles: Each angle in a rectangle is exactly 90 degrees.
• Rectangles are a type of parallelogram: Like all parallelograms, they have two pairs of parallel sides.

Understanding rectangles helps in comprehending their properties better, which is useful for calculating areas, perimeters, and even expanding to other shapes like squares and parallelograms.

Measurement

In mathematics, measurement is the process of quantifying an object's size, shape, or capacity. For rectangles, the key measurements include length, width, and perimeter.

• Length and Width: These are the two dimensions of a rectangle. Length is typically the longer side, while width is the shorter. However, the assignment of length and width can vary as long as consistency is maintained.
• Units of Measurement: Rectangles can be measured in various units, such as centimeters, meters, or inches. It's crucial to use the same unit when performing calculations.
• Precision is Key: Ensure that measurements are accurate, as small errors can significantly alter outcomes, particularly in projects requiring precision, such as engineering or architecture.

Mathematics Formula

Math formulas are predetermined expressions that allow us to solve problems systematically and accurately. For a rectangle, the formula for calculating the perimeter is essential.

Formula for Perimeter

The perimeter of a rectangle is calculated with the formula:
\[ P = 2 imes (l + w) \]where \( P \) is the perimeter, \( l \) is the rectangle's length, and \( w \) is its width.

• Combining Concepts: By understanding both the properties of rectangles and accurate measurements, using formulas becomes straightforward.
• Importance in Problem Solving: Formulas let you break down problems into manageable steps, enhancing understanding and accuracy.
• Versatility: The perimeter formula isn't only for math class – it finds use in real-world scenarios, like calculating fencing needed for a rectangular garden.

Applying the formula effectively ensures proper computation of the perimeter, which aids in solving geometric problems efficiently.