Calculating the Length, Perimeter, and Area of a Rectangle Given a Side Ratio

This article explains how to calculate the length, perimeter, and area of a rectangle when the sides are in a given ratio and the width is specified. Using the example of a rectangle with a side ratio of 4:5 and a width of 28 inches, we will walk through the process step-by-step.

Introduction

A rectangle is a quadrilateral with four right angles, and its sides are represented by their lengths and widths. When the ratio of the sides is given, and the width is specified, we can determine the length, perimeter, and area of the rectangle.

Problem Statement

The sides of the rectangle are in the ratio of 4:5, and the width is 28 inches. We need to find the length, perimeter, and area of the rectangle.

Step-by-Step Solution

Step 1: Calculate the Length

Given that the ratio of the sides is 4:5, we can say:

Width 4x, where x is a constant.

Solving for x:

Width 4x 28 inches. Therefore:

x 28 / 4 7 inches

Now, we can find the length:

Length 5x 5 * 7 35 inches

Step 2: Calculate the Perimeter

The perimeter of a rectangle is given by:

Perimeter 2(Length Width)

Substituting the values:

Perimeter 2(35 28) 2 * 63 126 inches

Step 3: Calculate the Area

The area of a rectangle is calculated by:

Area Length * Width

Substituting the values:

Area 35 * 28 980 square inches

Summary of Results

Length: 35 inches

Perimeter: 126 inches

Area: 980 square inches

Conclusion

Using the given ratio of 4:5 and a width of 28 inches, we have determined the length, perimeter, and area of the rectangle.

Formulae

Perimeter 2(Length Width) Area Length * Width

Frequently Asked Questions

What if the width is a different value? The process remains the same. Calculate the constant x, and then determine the length, perimeter, and area. Can the sides of a rectangle ever be in a ratio other than 4:5? Yes, the sides can be in any ratio. Just replace 4 and 5 with the given ratio in the formulae. Is there a calculator available for these calculations? While it is possible to use an online calculator, understanding the manual process is important for problem-solving and verifying results.

Keywords: rectangle, side ratio, width, length, perimeter, area