Problem 96 - Intermediate Algebra

Question

Answer the question with an algebraic expression. The perimeter of a square is \(i\) inches. What is the perimeter expressed in feet?

Step-by-Step Solution

Answer

\( \frac{i}{12} \)

Step 1: Understanding the Problem

The perimeter of a square is given in inches as \( i \). We need to convert this measurement from inches to feet while maintaining the perimeter as an algebraic expression.

Step 2: Conversion Factor

To convert inches to feet, we use the conversion factor: 1 foot = 12 inches. Therefore, we need to divide the given number of inches by 12 to convert it to feet.

Step 3: Applying the Conversion

Since the perimeter in inches is \( i \), the equivalent perimeter in feet can be found using the expression: \( \frac{i}{12} \). This divides the inches by the conversion factor to give us the measurement in feet.

Step 4: Solution Interpretation

The solution to the problem is the perimeter of the square expressed in feet, which is \( \frac{i}{12} \). This expression shows how the perimeter can be converted from inches to feet for any value of \( i \).

Key Concepts

Perimeter of a Square

To fully grasp the concept of converting a square's perimeter from inches to feet, it's important to start with understanding what the perimeter of a square means. The perimeter is the total distance around the square. For a square, this is calculated by adding up the lengths of all four sides. Since all sides of a square are equal in length, you can calculate the perimeter by multiplying the length of one side by 4. Let's say each side of the square is represented by the variable 's'. Thus, the formula for perimeter (P) is: \[ P = 4s \] In the given problem, the perimeter is already provided as an algebraic expression in terms of 'i'. However, the key takeaway is always to remember that calculating perimeter involves understanding the shape you are working with and correctly applying the basic formula. With a solid foundation in what perimeter means, you can tackle various problems involving squares effortlessly.

Unit Conversion

Unit conversion is a fundamental concept in algebra and everyday life, as it allows us to translate measurements from one unit to another. Understanding how this works is crucial for solving real-world problems where measurements need to be compared or combined despite their different units. In the context of this problem, we need to convert the perimeter of a square from inches to feet. This requires knowing the conversion factor between inches and feet. The conversion factor between these units is 12, meaning that 12 inches equal 1 foot. To convert a measurement from inches to feet, use the following steps:

• Identify the measurement in inches (in this case, 'i').
• Divide the number of inches by the conversion factor (12).

By dividing by 12, you effectively translate the measure from a smaller unit (inches) to a larger unit (feet). Therefore, the perimeter in feet can be expressed as:\[ \frac{i}{12} \]This new expression lets you work more easily with measurements in feet, which might be more practical depending on the context of the problem. Remember, understanding and applying conversion factors is a skill that can be used in various situations beyond just this exercise.

Algebra Problems

Working through algebra problems involves recognizing patterns and applying logical steps to find solutions. In this exercise, we're dealing with an algebra problem that requires expressing a known perimeter in a different unit.Algebraic expressions are used to represent quantities in a general form, making them powerful tools for problem-solving. Here, the perimeter is given as \( i \) inches, which is already an algebraic expression. Our task is to manipulate this expression to account for a change in units.To do this, we use known algebraic operations—in this case, division by the conversion factor—to revise our expression. The key steps to dealing with algebra word problems include:

• Understanding what the problem is asking you to find.
• Identifying the known variables and constants.
• Applying algebraic rules and operations to manipulate expressions as needed.
• Reinterpreting the solution in the context of the question (interpreting \( \frac{i}{12} \) as feet).

Algebra problems like this develop your ability to think logically and to solve problems using mathematical principles. Always break down the problem into smaller parts, recognize relationships, and follow through with calculations to provide a solution.