Solving for the Dimensions of a Rectangular Field: A Comprehensive Guide

Understanding the dimensions and area of a rectangular field is crucial in many practical applications, such as land surveying, gardening, and construction. In this article, we will explore the process of determining the length and width of a rectangular field given its area and the ratio of its sides. This guide will illustrate step-by-step solutions and provide valuable insights for solving similar problems.

Introduction to Rectangular Fields

A rectangular field is a two-dimensional shape characterized by its length and width, both of which are perpendicular to each other. The area of a rectangle is calculated by multiplying its length by its width. This article focuses on a specific case where the area is 726 square meters and the sides are in the ratio 3:2.

Understanding the Given Information

We are given the area of a rectangular field as 726 square meters and the ratio of its length to its width as 3:2. Let's denote the length as 3x and the width as 2x, where x is a common multiplier.

Deriving the Side Lengths

1. Express the area formula using the given ratio: [ text{Area} text{length} times text{width} ] Substituting the given values: [ 3x times 2x 6x^2 ] 2. Set the expression equal to the given area: [ 6x^2 726 ] 3. Solve for (x^2): [ x^2 frac{726}{6} 121 ] 4. Take the square root of both sides to solve for (x): [ x sqrt{121} 11 ] 5. Substitute (x) back into the expressions for length and width: [ text{Length} 3x 3 times 11 33 text{ meters} ] [ text{Width} 2x 2 times 11 22 text{ meters} ] Thus, the dimensions of the rectangular field are 33 meters by 22 meters.

Application and Importance

Understanding and applying these calculations is not just academic; it has practical implications in various fields. For instance, in agriculture, knowing the exact dimensions of a field can help in planing crops, managing irrigation, and determining the required amount of fertilizers. In construction, accurate dimensions are essential for project planning and cost estimation.

Conclusion

Solving for the dimensions of a rectangular field with a given area and side ratio is a straightforward process when understood with a systematic approach. This article has demonstrated the method through a step-by-step solution, providing a clear methodology that can be applied to similar problems. By mastering these concepts, one can efficiently tackle real-world problems involving rectangular fields.

Keywords

rectangular field, area calculation, ratio of sides, geometry