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Chapter 2: Problem 87

The total length of the four sides of a square is \(18.8\) centimeters. How long is each side of the square?

Short Answer

Expert verified
Each side of the square is 4.7 cm long.

Step by step solution

01

Understanding the Problem

We are given that the total length of the four sides of a square is 18.8 centimeters. Each side of a square is of equal length, and we need to find the length of one side.
02

Setting up the Equation

Let the length of each side of the square be represented by \(s\). Since a square has four equal sides, the total perimeter can be described by the equation \(4s = 18.8\) centimeters.
03

Solving for the Side Length

To find \(s\), divide both sides of the equation \(4s = 18.8\) by 4. This gives \(s = \frac{18.8}{4}\).
04

Calculating the Result

Perform the division: \(s = 4.7\). This is the length of each side of the square in centimeters.

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Key Concepts

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

Solving Equations
In elementary algebra, solving equations is a fundamental skill. It involves finding the value of a variable that makes the equation true. In the given exercise, we have the equation \(4s = 18.8\), representing the perimeter of a square. Here, \(s\) denotes the length of one side of the square.

To solve for \(s\):
  • Understand that the perimeter equation \(4s = 18.8\) indicates four sides of equal length adding to a total of 18.8 centimeters.
  • Isolate \(s\) by performing the same operation鈥攄ivision in this case鈥攐n both sides of the equation.
  • Divide both sides by 4 to simplify, giving \(s = \frac{18.8}{4}\).
This process of isolating the variable by performing inverse operations is a crucial technique for solving linear equations.
Perimeter of a Square
The perimeter is the total distance around a shape. For squares, this is particularly simple due to their geometry. A square has four sides of equal length. Therefore, its perimeter is calculated by multiplying the length of one side by 4.

In the exercise:
  • The perimeter is known to be 18.8 centimeters and is equated to \(4s\), where \(s\) is the length of a side.
  • Understanding this relationship allows us to write the equation \(4s = 18.8\).
  • Solving this equation helps us determine the value of each side of the square, crucial for understanding this geometric property.
This concept forms the foundation for calculating perimeters of all regular polygons, highlighting the efficiency of algebraic expressions.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. These are the building blocks of mathematics. In our problem, division is used prominently to isolate and determine the unknown side \(s\) of the square.

Key operation in the exercise:
  • Once we know that the perimeter equation is \(4s = 18.8\), division allows us to solve for \(s\).
  • Dividing both sides by 4 helps us find \(s = \frac{18.8}{4} = 4.7\).
  • This arithmetic operation effectively finds the value needed, showcasing the power of basic arithmetic in problem-solving.
Understanding and practicing these operations are essential for solving various equations in more advanced mathematics.

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Most popular questions from this chapter

Perform the indicated operations. $$(-0.7)(-64)$$

Evaluate each algebraic expression for the given values of the variables. Don't forget that for some problems it might be helpful to combine similar terms first and then to evaluate. \(\frac{3}{5} y-\frac{2}{3} y-\frac{7}{15} y \quad\) for \(y=-\frac{5}{2} \quad \frac{4}{3}\)

(a) How can we tell that \(\frac{5}{16}\) will produce a terminating decimal? (b) How can we tell that \(\frac{7}{15}\) will not produce a terminating decimal? (c) Determine which of the following will produce a terminating decimal: \(\frac{7}{8}, \frac{11}{16}, \frac{5}{12}, \frac{7}{24}, \frac{11}{75}, \frac{13}{32}, \frac{17}{40}\), \(\frac{11}{30}, \frac{9}{20}, \frac{3}{64} .\)

Simplify each algebraic expression by combining similar terms. $$5.4 n-0.8 n-1.6 n$$

Perform the indicated operations. $$(0.4)(2.9)$$
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