Solving for the Length of a Rectangle Given Perimeter and Breadth

In this article, we will explore how to solve for the length of a rectangle when we know its perimeter and breadth. The perimeter of a rectangle can be calculated using the formula:

Perimeter Formula for a Rectangle

The perimeter P of a rectangle is calculated by using the following formula:

P 2(L B), where

P is the perimeter, L is the length, B is the breadth.

This formula allows us to find the length of the rectangle when the perimeter and breadth are known. Let's go through an example to understand this better.

Example Problem

Suppose, the perimeter of a rectangle is 100 cm and its breadth is 30 cm. What is the length of the rectangle?

Step-by-Step Solution

Identify the given values:

Perimeter P 100 cm, Breadth B 30 cm.

Write down the formula for the perimeter of a rectangle:

P  2(L   B)

Substitute the given values into the formula:

100  2(L   30)

Rearrange the equation to solve for length L:

100  2L   60100 - 60  2L40  2L

Divide both sides by 2 to isolate L:

L  40/2  20

Thus, the length of the rectangle is 20 cm.

Verification

To verify our solution, let's check the perimeter using the calculated length:

Calculation

P 2(L B) 2(20 30) 2(50) 100 cm

The perimeter indeed matches the given value, confirming our solution is correct.

Another Example

Let's consider another example for further clarity. If the perimeter of a rectangle is 180 cm and the breadth is 40 cm, what would be the length?

Step-by-Step Solution

Given values:

Perimeter P 180 cm, Breadth B 40 cm.

Write down the formula for the perimeter of a rectangle:

P  2(L   B)

Substitute the given values into the formula:

180  2(L   40)

Rearrange the equation to solve for length L:

180  2L   80180 - 80  2L100  2L

Divide both sides by 2 to isolate L:

L  100/2  50

Thus, the length of the rectangle is 50 cm.

Conclusion

By using the perimeter formula of a rectangle, we can easily solve for its length when the perimeter and breadth are known. This is a fundamental concept in geometry and is widely applicable in various practical scenarios, such as designing and construction projects.

Additional Resources

For more detailed information on geometry, perimeter calculations, and real-world applications, consider checking out these resources:

Geometry Perimeter Calculator (MathisFun) Khan Academy - Perimeter and Area Review