Solving for Rectangle Dimensions Given a Specific Side Ratio and Perimeter

In geometry, understanding the dimensions of a rectangle based on given ratios and the perimeter is a common problem. This article will demonstrate a step-by-step method to solve such a problem. Let's explore how to find the sides of a rectangle when the ratio of its sides is 2:3 and the perimeter is 480 units.

Problem Statement

A rectangle has a ratio of its sides as 2:3 and a perimeter of 480 units. What are the sides of the rectangle?

Solution

Let's start by setting up the problem with the given information. We know the ratio of the sides of the rectangle is 2:3. Let's denote the breadth (shorter side) as 2x units and the length (longer side) as 3x units. Given that the perimeter of the rectangle is 480 units, we can write this as:

Using the Perimeter Formula

The formula for the perimeter (P) of a rectangle is given by:

P 2(l w)

Where l is the length and w is the width. Substituting the given values:

480 2(3x 2x)

Simplifying the equation:

480 2(5x)

480 1

Solving for x:

x 480 / 10

x 48

Now that we have the value of x, we can find the exact dimensions of the rectangle.

The breadth is:

2x 2 * 48 96 units

The length is:

3x 3 * 48 144 units

Verification

To confirm the correctness of our solution, let's verify it using the perimeter formula:

Perimeter 2(Length Breadth)

Perimeter 2(144 96) 2(240) 480 units

The solution holds true as the perimeter matches the given value.

Summary

In this problem, we were given the ratio of the sides of a rectangle (2:3) and its perimeter (480 units). By setting up the equation based on the formula for the perimeter of a rectangle and solving for the unknown variable x, we were able to determine the exact dimensions of the rectangle. The breadth and length of the rectangle are 96 units and 144 units, respectively.

Conclusion

Understanding the relationship between the ratio of the sides and the perimeter of a rectangle is a valuable skill in geometry. This problem demonstrates a practical application of such knowledge. By breaking down the problem into manageable steps and using the appropriate formulas, we can solve such problems efficiently.

Related Keywords

For further exploration and practice, you can try solving similar problems or refer to resources and tutorials on geometry.