Determining the Dimensions of a Rectangular Swimming Pool Using Perimeter and Length-Breadth Relationship

In this article, we will explore how to determine the length and breadth of a rectangular swimming pool, given its perimeter and the relationship between its length and breadth. This problem is a great example of applying basic algebra to solve real-world geometric problems. Let's dive into the steps to find the solution.

Problem Statement

The perimeter of a rectangular swimming pool is 154 meters. Its length is 2 meters more than twice its breadth. The task is to find the length and breadth of the pool.

Step-by-Step Solution

Step 1: Define Variables

Let us define the variables:

The breadth of the swimming pool as b meters. The length of the swimming pool as l meters.

Step 2: Use the Perimeter Formula

The perimeter P of a rectangle is given by:

P 2(l b)

Given that the perimeter P 154 meters: Substituting the formula for the perimeter:

2(l b) 154

Dividing both sides by 2:

l b 77 ... (Equation 1)

Step 3: Use the Length-Breadth Relationship

It is given that the length of the swimming pool is 2 meters more than twice its breadth. This can be expressed as:

l 2b 2 ... (Equation 2)

Step 4: Substitute and Solve the System of Equations

Substitute Equation 2 into Equation 1:

(2b 2) b 77

Combine like terms:

3b 2 77

Subtract 2 from both sides:

3b 75

Divide by 3:

b 25

Now, use Equation 2 to find the length:

l 2(25) 2 50 2 52 meters

Conclusion

The dimensions of the swimming pool are:

Breadth: 25 meters Length: 52 meters

Summary

In summary, we have used algebraic methods to solve a real-world problem involving the perimeter and dimensions of a rectangular swimming pool. This type of problem is a good example of how mathematical concepts can be applied to practical situations.

Additional Resources

For more information on similar problems or for advanced mathematical concepts, visit the following resources:

Solving Systems of Linear Equations Rectangular Swimming Pools: Length, Breadth, and Diagonal Solving Systems of Linear Equations Using Substitution