How to Calculate the Length of a Rectangle Given Its Perimeter and Breadth

Understanding the relationship between the perimeter, length, and breadth of a rectangle is a fundamental concept in geometry. This article will guide you through the process of calculating the length of a rectangle when you know its perimeter and breadth. We will provide step-by-step solutions and further explain the relevant formulas to ensure a clear understanding.

Understanding the Perimeter and Breadth of a Rectangle

The perimeter (P) of a rectangle is the total distance around the outside of the rectangle. This distance can be calculated using the formula:

Perimeter Formula: ( P 2 times (L B) )

where ( P ) is the perimeter, ( L ) is the length, and ( B ) is the breadth (or width) of the rectangle.

Given Problem: Rectangle with Perimeter 44 cm and Breadth 8 cm

Let's solve the problem where the perimeter of a rectangle is 44 cm and the breadth is 8 cm. We are asked to find the length (L).

Step-by-Step Solution

1. Start with the perimeter formula:

$$ P 2 times (L B) $$

2. Substitute the known values into the formula:

$$ 44 2 times (L 8) $$

3. Simplify the equation:

$$ 44 2L 16 $$

4. Subtract 16 from both sides to isolate the term with L:

$$ 44 - 16 2L $$

$$ 28 2L $$

5. Divide both sides by 2 to solve for L:

$$ L frac{28}{2} $$

$$ L 14 text{ cm} $$

So, the length of the rectangle is 14 cm.

Alternative Solutions

Another approach to solving this problem involves the following steps:

Start with the equation based on the perimeter formula: Substitute the known values: Simplify and solve for the length: Conclude the length of the rectangle.

For example:

Given: Perimeter (P) 44 cm, Breadth (B) 8 cm Write the equation: 44 2L 16 Solve for L: 28 2L > L 14 cm

Additional Resources

For further learning, you can watch the mathfry YouTube channel for videos explaining basic math concepts, including geometric formulas and problem-solving techniques.

Remember, mastering the formulas and understanding the steps involved will greatly enhance your problem-solving skills in geometry. Whether you are a student or an adult looking to brush up on your math skills, you will find these resources valuable and informative.

Keywords: rectangle perimeter, rectangle length, perimeter formula