Solving for the Dimensions of a Rectangle with a Perimeter of 146 Centimeters

In geometry, understanding the relationship between the length and width of a rectangle, as well as its perimeter, is a fundamental concept. Let's explore how to find the dimensions of a rectangle where the length is 5 less than twice the width, and the perimeter is 146 centimeters.

Problem Statement

The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, what are the dimensions of it?

Variables and Relationships

Let w width in centimeters.
L length 2w - 5 centimeters
Perimeter P 2L 2w 146 centimeters.

Steps to Solve the Problem

1. Express the length in terms of width:

L 2w - 5

2. Substitute the length into the perimeter formula:

P 2L 2w

146 2(2w - 5) 2w

3. Simplify the equation:

146 4w - 10 2w

146 6w - 10

4. Solve for width:

146 10 6w

156 6w

26 w

5. Calculate the length:

L 2w - 5

L 2(26) - 5

L 52 - 5

L 47

Verification

To ensure the solution is correct, substitute the width and length back into the perimeter formula:

P 2L 2w
P 2(47) 2(26)
P 94 52
P 146 centimeters

The dimensions of the rectangle are 47 centimeters by 26 centimeters.

Additional Practice

If you need practice solving similar problems or want to explore the concept further, you can visit the following resources:

Mathway Khan Academy Cuemath

Remember, the key to mastering geometry problems is consistent practice and understanding the underlying principles. Happy problem-solving!