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What is the formula to calculate the perimeter of a rectangle?

Published in Geometry Formulas 3 mins read

The formula to calculate the perimeter of a rectangle is P = (L + W) × 2, where 'P' represents the perimeter, 'L' represents the length, and 'W' represents the width. This fundamental formula allows you to quickly determine the total distance around the outside edge of any rectangular shape, provided you know its length and width.

Understanding the Perimeter Formula

The perimeter of any two-dimensional shape is the total distance around its boundary. For a rectangle, which has four sides with opposite sides being equal in length, the perimeter is the sum of all its sides. Since a rectangle has two equal lengths and two equal widths, the formula simplifies this sum.

Here's a breakdown of the variables used in the formula:

Variable Represents Description
P Perimeter The total distance around the outside of the rectangle.
L Length The measurement of the longer side of the rectangle.
W Width The measurement of the shorter side of the rectangle.

The Concept Behind the Formula

A rectangle has two lengths and two widths. If you were to walk along its edges, you would cover one length, then one width, followed by another length, and finally another width to return to your starting point. This means the total distance is L + W + L + W. This sum can be simplified by combining like terms to 2L + 2W. Factoring out the common factor of 2 gives us the concise formula P = (L + W) × 2.

Applying the Formula: A Simple Example

To illustrate how to use the perimeter formula, let's consider a practical scenario. When you are given the dimensions of a rectangular shape, you can simply plug in the values of L and W into the formula in order to solve for the perimeter.

Scenario: You need to put a decorative border around a rectangular notice board that is 90 cm long and 60 cm wide. How much border material do you need?

Solution:

  1. Identify the given dimensions:
    • Length (L) = 90 cm
    • Width (W) = 60 cm
  2. Write down the perimeter formula:
    • P = (L + W) × 2
  3. Substitute the values into the formula:
    • P = (90 cm + 60 cm) × 2
  4. Perform the addition inside the parentheses first:
    • P = (150 cm) × 2
  5. Multiply by 2 to find the perimeter:
    • P = 300 cm

Therefore, you would need 300 cm of border material for your notice board.

Practical Applications of Calculating Perimeter

Understanding how to calculate the perimeter of a rectangle is a valuable skill with various real-world applications:

  • Home Improvement:
    • Measuring for fencing a backyard or garden.
    • Estimating the amount of baseboards needed for a room.
    • Sizing trim for windows, doors, or furniture.
  • Construction and Design:
    • Laying out the foundation for a building.
    • Calculating the amount of edging required for paths or driveways.
  • Crafts and Hobbies:
    • Determining the length of fabric borders for quilts or sewing projects.
    • Cutting framing material for pictures or artwork.
    • Measuring ribbons or decorative elements for gifts.

By simply plugging the length and width values into the formula P = (L + W) × 2, you can efficiently solve for the perimeter of any rectangular shape.