The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 1120 meters, what will be the area of the field?

Points to Remember:

The problem involves a rectangle with a relationship between breadth and length.
We need to find the length and breadth using the given perimeter.
The area of a rectangle is calculated as length Ã breadth.

Introduction:

This question is a mathematical word problem requiring a factual and analytical approach. It tests our understanding of the properties of rectangles (specifically the relationship between perimeter, length, breadth, and area) and our ability to solve simultaneous equations. A rectangle is a quadrilateral with four right angles. The perimeter is the total distance around the shape, while the area is the space enclosed within the shape.

Body:

1. Defining Variables and Setting up Equations:

Let’s denote the length of the rectangular field as ‘L’ meters and the breadth as ‘B’ meters. We are given that the breadth is 60% of the length, which can be expressed as:

B = 0.6L (Equation 1)

The perimeter of a rectangle is given by the formula: Perimeter = 2(L + B). We are given that the perimeter is 1120 meters:

2(L + B) = 1120 (Equation 2)

2. Solving for Length and Breadth:

We can now solve these two equations simultaneously. Substitute Equation 1 into Equation 2:

2(L + 0.6L) = 1120

2(1.6L) = 1120

3.2L = 1120

L = 1120 / 3.2 = 350 meters

Now, substitute the value of L back into Equation 1 to find B:

B = 0.6 * 350 = 210 meters

3. Calculating the Area:

The area of the rectangular field is calculated as:

Area = L Ã B = 350 meters Ã 210 meters = 73500 square meters

Conclusion:

In summary, by using the given information about the perimeter and the relationship between the length and breadth, we determined that the length of the rectangular field is 350 meters and the breadth is 210 meters. Therefore, the area of the field is 73500 square meters. This problem highlights the importance of understanding geometric formulas and applying algebraic techniques to solve real-world problems. No further policy recommendations or best practices are needed as this is a purely mathematical exercise. The solution demonstrates a clear and logical approach to problem-solving, emphasizing accuracy and precision in calculations.

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