Determining the Side Length of a Square Given its Perimeter

Introduction

A square, an essential shape in geometry, is defined by its four equal sides and four 90-degree angles. The perimeter of a square, which is the sum of the lengths of all its sides, is a fundamental measurement that helps in understanding the dimensions of the square. In this article, we will explore a practical example to determine the length of one side of a square given its perimeter.

Understanding Perimeter and Squares

Firstly, let’s clarify a few basic concepts related to squares and their perimeter.

A square is a plane figure with four sides of equal length and four right angles. The perimeter of a square, denoted as P, is the total length of all its sides. The formula for the perimeter of a square can be written as:

Perimeter (P) 4 × side length (s)

This formula highlights that the perimeter is four times the length of any one side of the square. Conversely, if you know the perimeter, you can determine the side length by dividing the perimeter by 4.

Solving a Practical Example

Let us consider a practical problem. Suppose we are given that the perimeter of a square is 212 centimeters. We need to determine the length of one side of the square.

Step-by-Step Solution

Given information: Perimeter (P) 212 cm Formula: Perimeter (P) 4 × side length (s) Rearrange the formula to find the side length: side length (s) P / 4 Substitute the given value into the formula: side length (s) 212 cm / 4 Calculate the side length: side length (s) 53 cm

Therefore, the length of one side of the square is 53 cm.

Proof of the Solution

To further validate the solution, let us verify it using the perimeter formula.

Substitute the calculated side length back into the perimeter formula:

Perimeter (P) 4 × 53 cm 212 cm

This confirms that the perimeter of the square is indeed 212 cm, thus proving our solution is correct.

In conclusion, the length of one side of the square is 53 cm.

Keywords: perimeter, square, side length