How to Calculate the Perimeter of a Rectangle with Double Dimensions: A Step-by-Step Guide

In this guide, you will learn how to calculate the perimeter of a rectangle where the length is twice the breadth and the area is given as 800 square units. We will explore the relationship between the dimensions and the calculations required to find the perimeter.

Understanding the Relationship Between Length and Breadth

The relationship given in the problem statement tells us that the length (L) of the rectangle is twice its breadth (B). This gives us the equation:

L 2B

Using the Area to Find the Breadth and Length

The area of a rectangle is given by the formula:

A L times; B

Given that the area (A) is 800 square units, we can substitute the value of L from the previous step into this formula:

800 2B times; B

Which simplifies to:

800 2B2

To solve for B, we divide both sides by 2:

400 B2

Then we take the square root of both sides:

B √400

B 20

Given that the length is twice the breadth, we calculate the length (L) as:

L 2B

L 2 times; 20

L 40

Calculating the Perimeter of the Rectangle

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

P 2L 2B

Substituting the values of L and B from the previous calculations:

P 2 times; 40 2 times; 20

P 80 40

P 120

Therefore, the perimeter of the rectangle is 120 units.

Understanding the Effect of Doubling Dimensions

It’s also worth noting that if both length and breadth are doubled, the new perimeter will be four times the original perimeter because the perimeter formula is linear in terms of L and B.

Using the general formula for the perimeter of a rectangle, if L and B are doubled, the perimeter is revised to:

2(2L) 2(2B) 4L 4B

This is effectively four times the original perimeter (2L 2B).

Conclusion

The perimeter of the rectangle is 120 units. This calculation demonstrates how to use the relationship between length and breadth, as well as the area, to determine both dimensions and, subsequently, the perimeter of a rectangle.