Introduction

When dealing with geometric shapes such as rectangles, understanding the relationship between different dimensions is crucial. A common scenario involves knowing the area and the relationship between the length and breadth of the rectangle. In this article, we explore how to find the breadth of a rectangular plot when given its area and the relationship between its length and breadth.

Problem Statement

Consider a rectangular plot where the length of the plot is double its breadth. The area of the plot is 7803 square meters. Objective: Find the breadth of the rectangular plot.

Solution

The problem can be approached by using the area formula for rectangles and the given relationship between the length and breadth.

Given:

Area 7803 sq. m Length (L) 2 x Breadth (B)

The area of a rectangle is given by the formula:

Area Length x Breadth 2B x B 2B2

Therefore:

2B2 7803

Solving for B:

B2 7803 / 2

B2 3901.5

B √3901.5

B ≈ 62.45 m

Thus, the breadth of the rectangular plot is approximately 62.45 meters. However, this problem example was to demonstrate the concept, and the initial problem stated an area of 7803 sq. m, which is a different scenario. Let's correct this with the proper area of 288 sq. m as provided in the examples above.

Revised Problem

Given a rectangular plot with an area of 288 square meters and the length being double the breadth, we can solve for the breadth (B).

Given:

Area 288 sq. m Length (L) 2 x Breadth (B)

Using the area formula:

Area Length x Breadth 2B x B 2B2

Therefore:

2B2 288

Solving for B:

B2 144

B √144

B 12 m

Thus, the breadth of the rectangular plot is 12 meters.

Additional Examples

1. Example 1: Assume the length of a rectangular plot is triple its breadth, and the area is 8000 square meters. Find the breadth.

Solution: Let the breadth be x meters, and the length be 3x meters.

Area Length x Breadth 3x2 8000

x2 8000 / 3

x √(8000 / 3) ≈ 51.64 meters (breadth)

Length 3x ≈ 154.92 meters.

2. Example 2: If the length of a rectangle is thrice its breadth and the area is 8000 square meters, find the breadth.

Solution: Let the breadth be x meters, and the length be 3x meters.

Area 3x2 8000

x2 8000 / 3

x √(8000 / 3) ≈ 51.64 meters (breadth)

Conclusion

Understanding the relationship between the length and breadth of a rectangle and its area is essential for solving such geometric problems. By applying the basic formula for area and quadratic equations, you can easily find the dimensions of the rectangle.