Understanding the Perimeter of a Rectangle with a 9:5 Ratio

When dealing with a rectangle, the perimeter is a fundamental concept that measures the total length of its boundary. The formula for calculating the perimeter of a rectangle is given by:

Perimeter 2(length breadth)

Given Problem: The Length and Breadth Ratio is 9:5

Let's break down the problem step by step. Suppose the length and breadth of the rectangle are in the ratio 9:5. We can express the length as 9x and the breadth as 5x, where x is a common factor.

Step 1: Formulating the Perimeter with Variable x

The perimeter of the rectangle, in terms of x, can be written as follows:

Perimeter 2(9x 5x) 2(14x) 28x units

Step 2: Given Perimeter in Units

Suppose the perimeter of the rectangle is given as 364 units. We can set up the equation:

28x 364

Solving for x:

x 364 / 28 13

Step 3: Calculating the Actual Dimensions

Now that we know x 13, we can calculate the actual length and breadth:

Thus, the length and breadth of the rectangle are 117 units and 65 units, respectively.

Step 4: Calculating the Perimeter

Using these dimensions, the perimeter can be calculated as:

Perimeter 2(117 65) 2(182) 364 units

This confirms our initial condition that the perimeter is 364 units.

Conclusion

The key to solving such problems lies in expressing the length and breadth in terms of a common factor, solving the linear equation, and then calculating the actual dimensions. This method ensures that we arrive at the correct perimeter and dimensions for the rectangle.