The Breadth Of A Rectangle Is 1 By 5 Of Its Perimeter If The Perimeter Of A Rectangle Is 100 M Find Its Length
The Breadth of a Rectangle: Understanding the Relationship Between Perimeter and Dimensions
In geometry, the perimeter of a rectangle is the total length of its boundary. It is calculated by adding the lengths of all four sides. The perimeter of a rectangle is given by the formula: P = 2(l + b), where P is the perimeter, l is the length, and b is the breadth. In this article, we will explore the relationship between the perimeter and the dimensions of a rectangle, specifically the breadth, which is 1/5 of its perimeter.
Let's start by understanding the relationship between the perimeter and the breadth of a rectangle. We are given that the breadth of the rectangle is 1/5 of its perimeter. Mathematically, this can be represented as:
b = (1/5)P
where b is the breadth and P is the perimeter.
Given Perimeter: 100 m
We are given that the perimeter of the rectangle is 100 m. We can substitute this value into the equation above to find the breadth:
b = (1/5) × 100 b = 20 m
Now that we have the breadth, we can use the formula for the perimeter to find the length. The formula for the perimeter is:
P = 2(l + b)
We know the perimeter (P = 100 m) and the breadth (b = 20 m). We can substitute these values into the formula to find the length:
100 = 2(l + 20) 100 = 2l + 40 60 = 2l 30 = l
Therefore, the length of the rectangle is 30 m.
In this article, we explored the relationship between the perimeter and the dimensions of a rectangle, specifically the breadth, which is 1/5 of its perimeter. We used the formula for the perimeter to find the breadth and then used the breadth to find the length. The length of the rectangle is 30 m.
Key Takeaways
- The breadth of a rectangle is 1/5 of its perimeter.
- The formula for the perimeter is P = 2(l + b).
- We can use the formula for the perimeter to find the breadth and then use the breadth to find the length.
Example Problems
- Find the breadth of a rectangle with a perimeter of 120 m.
- Find the length of a rectangle with a breadth of 15 m and a perimeter of 150 m.
Solutions
- b = (1/5) × 120 b = 24 m
- 150 = 2(l + 15) 150 = 2l + 30 120 = 2l 60 = l
Therefore, the breadth of the rectangle is 24 m and the length is 60 m.
Real-World Applications
The relationship between the perimeter and the dimensions of a rectangle has many real-world applications. For example, in architecture, the perimeter of a building is an important factor in determining the amount of materials needed for construction. In engineering, the perimeter of a pipe or a tube is an important factor in determining the amount of material needed for manufacturing.
In conclusion, the relationship between the perimeter and the dimensions of a rectangle is an important concept in geometry. We can use the formula for the perimeter to find the breadth and then use the breadth to find the length. This concept has many real-world applications and is an important tool for architects, engineers, and other professionals.
The Breadth of a Rectangle: Q&A
In our previous article, we explored the relationship between the perimeter and the dimensions of a rectangle, specifically the breadth, which is 1/5 of its perimeter. We used the formula for the perimeter to find the breadth and then used the breadth to find the length. In this article, we will answer some frequently asked questions about the breadth of a rectangle.
Q: What is the breadth of a rectangle with a perimeter of 200 m? A: To find the breadth, we can use the formula: b = (1/5)P. Substituting the value of the perimeter, we get: b = (1/5) × 200 = 40 m.
Q: How do I find the length of a rectangle with a breadth of 20 m and a perimeter of 120 m? A: We can use the formula for the perimeter to find the length. First, we need to find the sum of the length and breadth: l + b = (P/2) = (120/2) = 60. Then, we can subtract the breadth from the sum to find the length: l = 60 - 20 = 40 m.
Q: What is the breadth of a rectangle with a length of 30 m and a perimeter of 180 m? A: We can use the formula for the perimeter to find the breadth. First, we need to find the sum of the length and breadth: l + b = (P/2) = (180/2) = 90. Then, we can subtract the length from the sum to find the breadth: b = 90 - 30 = 60 m.
Q: How do I find the perimeter of a rectangle with a length of 40 m and a breadth of 20 m? A: We can use the formula for the perimeter: P = 2(l + b). Substituting the values of the length and breadth, we get: P = 2(40 + 20) = 2(60) = 120 m.
Q: What is the breadth of a rectangle with a perimeter of 150 m and a length of 30 m? A: We can use the formula for the perimeter to find the breadth. First, we need to find the sum of the length and breadth: l + b = (P/2) = (150/2) = 75. Then, we can subtract the length from the sum to find the breadth: b = 75 - 30 = 45 m.
Q: How do I find the length of a rectangle with a breadth of 25 m and a perimeter of 200 m? A: We can use the formula for the perimeter to find the length. First, we need to find the sum of the length and breadth: l + b = (P/2) = (200/2) = 100. Then, we can subtract the breadth from the sum to find the length: l = 100 - 25 = 75 m.
In this article, we answered some frequently asked questions about the breadth of a rectangle. We used the formula for the perimeter to find the breadth and then used the breadth to find the length. We hope that this article has been helpful in understanding the relationship between the perimeter and the dimensions of a rectangle.
Key Takeaways
- The breadth of a rectangle is 1/5 of its perimeter.
- The formula for the perimeter is P = 2(l + b).
- We can use the formula for the perimeter to find the breadth and then use the breadth to find the length.
Example Problems
- Find the breadth of a rectangle with a perimeter of 220 m.
- Find the length of a rectangle with a breadth of 15 m and a perimeter of 180 m.
- Find the breadth of a rectangle with a length of 40 m and a perimeter of 160 m.
- Find the length of a rectangle with a breadth of 20 m and a perimeter of 140 m.
Solutions
- b = (1/5) × 220 = 44 m
- 180 = 2(l + 15) 180 = 2l + 30 150 = 2l 75 = l
- 160 = 2(l + 40) 160 = 2l + 80 80 = 2l 40 = l
- 140 = 2(l + 20) 140 = 2l + 40 100 = 2l 50 = l
Therefore, the breadth of the rectangle is 44 m, the length is 75 m, the breadth is 60 m, and the length is 40 m.