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Chapter 9: Problem 26

Solve. Find the perimeter of a square ceramic tile with a side of length 3 inches.

Short Answer

Expert verified
The perimeter is 12 inches.

Step by step solution

01

Understand the Problem

The problem requires finding the perimeter of a square tile. A square has four equal sides.
02

Recall the Perimeter Formula for a Square

The perimeter of a square is calculated using the formula \( P = 4s \), where \( s \) is the length of a side.
03

Substitute the Given Side Length into the Formula

Here, the side length \( s \) is given as 3 inches. Substitute this value into the formula: \( P = 4 \times 3 \).
04

Calculate the Perimeter

Perform the multiplication: \( 4 \times 3 = 12 \). Therefore, the perimeter is 12 inches.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding a Square
A square is a special type of quadrilateral that has several unique properties. One of the most important characteristics of a square is that all four sides are equal in length. This means that if you know the length of one side, you automatically know the length of all sides.
Additionally, a square has four right angles, each measuring 90 degrees. The diagonals of a square are equal in length and bisect each other at right angles.
These symmetrical properties make calculations involving squares straightforward and predictable. Because of these attributes, squares are often used in various mathematical problem-solving situations, making them a fundamental shape in geometry.
The Perimeter Formula for a Square
The perimeter of any geometric figure is the total length around the figure. For a square, this is the sum of the lengths of all its sides.
Since a square has four equal sides, its perimeter can be easily calculated using the formula: \[ P = 4s \]where \( P \) stands for the perimeter, and \( s \) is the length of one side.
This formula simplifies the calculation as you only need to know the length of one side to find the perimeter of the entire square. By multiplying the side length by four, you get the perimeter in just one step.
This straightforwardness is why understanding the perimeter formula prepares the ground for solving more complex problems.
Mathematical Problem-Solving Strategies
Solving mathematical problems is a skill that improves with practice and involves several strategies. Understanding the problem is the first crucial step. Read the question carefully to determine what is being asked and identify what information is given.
Next, recalling or identifying the right formula or method to use is important. In problems involving geometry, knowing the formulas for area, perimeter, and volume of shapes is essential.
  • Substitute the given values into the formula.
  • Perform calculations carefully, step by step.
  • Always double-check your work to confirm accuracy.
Finally, interpret your result to ensure it makes sense in the context of the problem.
Effective problem-solving involves a logical approach and often these techniques can be applied broadly across various types of mathematical problems.

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