How to Calculate the Length of a Rectangle Given Its Perimeter and Breadth

Understanding the relationship between the perimeter, length, and breadth of a rectangle is a fundamental concept in geometry. If you know the perimeter of a rectangle and its breadth, you can calculate the length. Let's explore how to do this step by step using an example.

The Formula for the Perimeter of a Rectangle

The perimeter of a rectangle is defined as the total distance around its edges. Mathematically, it can be expressed as:

P 2 L 2 B, where P is the perimeter, L is the length, and B is the breadth.

Example Calculation

Suppose a rectangle has a perimeter of 80 cm and a breadth of 4 cm. To find the length, follow these steps:

Step 1: Write Down the Given Information

Step 2: Substitute the Values into the Perimeter Formula

Using the formula P 2 L 2 B and substituting the given values:

80 2 L 2 * 4

Step 3: Simplify the Equation

Simplify the right side of the equation:

80 2 L 8

Step 4: Isolate the Variable L

Subtract 8 from both sides of the equation:

80 - 8 2 L

72 2 L

Divide both sides by 2:

L 72 / 2

L 36 cm

Conclusion

The length of the rectangle is 36 cm.

Understanding the Calculation

The first step in solving for the length of a rectangle given its perimeter and breadth is to recognize and apply the perimeter formula. Once the formula is set up, the next step is to simplify and isolate the variable L. This process involves basic algebraic operations such as subtraction and division.

Alternative Method

Another way to approach the problem is to recognize that the perimeter is the sum of all sides of the rectangle. Thus, if the breadth is 4 cm and the perimeter is 80 cm, you can subtract the total length of the two breadths from the perimeter:

80 - 4 * 2 72

This result, 72 cm, is twice the length of one side of the rectangle, so the length is 72 / 2 36 cm.

Conclusion

Understanding the relationship between the perimeter, length, and breadth of a rectangle is crucial in geometry. By following the steps outlined in this article, you can easily calculate the length of a rectangle given its perimeter and breadth. This concept is not only applicable to academic geometry but also to real-world applications such as construction, design, and packaging.

Keywords

rectangle perimeter, length calculation, breadth and perimeter

By following these steps, you can easily solve similar problems involving the perimeter of a rectangle. Practice with different values to solidify your understanding and confidence in performing these geometric calculations.