Determined Math: Calculating the Perimeter and Area of a Rectangle with Given Length and Width

Introduction

Determining the perimeter and area of a rectangle given specific dimensions is a fundamental concept in geometry. This article delves into the calculation of the perimeter and area of a rectangle where the length is 3 cm more than its width, specifically when the width is 6 cm. By following a structured approach, we can easily find the required measurements.

Problem Statement

The problem at hand involves a rectangle where the length is 3 cm more than its width, and the width is given as 6 cm. We need to find the perimeter and area of this rectangle.

Calculate the Length

To begin, we identify the given information:

The width ( b ) of the rectangle is 6 cm. The length ( l ) is 3 cm more than the width.

From the given information, we can express the length mathematically as:

Length ( l b 3 )

Substituting the width ( b 6 ) cm into the equation:

Length ( l 6 3 9 ) cm

Calculate the Perimeter

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

Perimeter ( P 2l 2b )

Substituting the values of ( l 9 ) cm and ( b 6 ) cm into the formula:

Perimeter ( P 2(9) 2(6) 18 12 30 ) cm

Thus, the perimeter of the rectangle is 30 cm.

Calculate the Area

The area ( A ) of a rectangle is given by the formula:

Area ( A l times b )

Substituting the values of ( l 9 ) cm and ( b 6 ) cm into the formula:

Area ( A 9 times 6 54 ) square cm

Therefore, the area of the rectangle is 54 square cm.

Conclusion

By systematically analyzing the given dimensions and applying the formulas for perimeter and area, we have successfully determined that the perimeter of the rectangle is 30 cm and the area is 54 square cm.

This detailed breakdown not only provides the correct answers but also helps in understanding the relationship between dimensions and geometric properties of a rectangle.