Solving for the Length of a Rectangle Given Its Perimeter and Breadth

Understanding the relationship between the length and breadth of a rectangle and its perimeter is a fundamental skill in geometry. In this article, we will explore how to find the length of a rectangle when given the breadth and its perimeter. Let's consider the problem: if the breadth of a rectangle is 10 meters and its perimeter is 60 meters, what is its length?

Given Information

Breadth of the rectangle 10 meters (b) Perimeter of the rectangle 60 meters (P) Length of the rectangle 2 × Breadth (l 2b)

Formula for Perimeter of a Rectangle

The formula to calculate the perimeter (P) of a rectangle is:

P 2l 2b

Substituting Given Values

Substitute the length (l 2b) and the given perimeter (P 60) into the formula:

60 2(2b) 2b

Simplify the equation:

60 4b 2b

60 6b

Calculating the Breadth

Solve for the breadth (b):

b 60 / 6 10 meters

Determining the Length

Substitute the breadth (b 10) back into the length equation (l 2b):

l 2 × 10 20 meters

Verification

Verify the solution by substituting the values back into the perimeter formula:

Perimeter (P) 2l 2b

P 2 × 20 2 × 10

P 40 20 60 meters

This confirms that our calculations are correct.

Additional Example

Consider another problem: if the breadth of a rectangle is 15 meters and its perimeter is 90 meters, what is its length?

Solving the Additional Example

Breadth of the rectangle 15 meters (b) Perimeter of the rectangle 90 meters (P) Length of the rectangle 3 × Breadth (l 3b)

Substitute the values into the perimeter formula:

90 2l 2b

90 2(3b) 2b

90 6b 2b

90 8b

Solve for the breadth (b):

b 90 / 8 11.25 meters

Substitute back into the length equation (l 3b):

l 3 × 11.25 33.75 meters

Conclusion

By following a systematic approach, you can easily solve problems involving the length and perimeter of a rectangle. Understanding these relationships is crucial in geometry and can be applied in various real-world scenarios.