How Do You Calculate the Perimeter of a Rectangle Step by Step?
The concept of perimeter of rectangle plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding how to find the perimeter of a rectangle is especially useful for solving geometry questions, practical problems like fencing and framing, and is a crucial topic in school maths curricula.
What Is Perimeter of Rectangle?
A perimeter of rectangle is defined as the total length around the boundary of a rectangle. Simply put, if you walk along all four sides of a rectangle, the distance you travel is its perimeter. You’ll find this concept applied in areas such as fencing fields, calculating border lengths, and measuring frames for photos or paintings.
Key Formula for Perimeter of Rectangle
Here’s the standard formula:
\(\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})\)
This can be written as \(P = 2(l + b)\), where “l” stands for length and “b” stands for breadth (or width). The result is always in units of length (such as cm, m, or inches).
Cross-Disciplinary Usage
Perimeter of rectangle is not only useful in Maths but also plays an important role in Science (e.g. Physics for circuits), Computer Science (graphics), and daily logical reasoning. Students preparing for exams like Olympiads, JEE, and board tests will regularly see this formula and applications in various question types.
Step-by-Step Illustration
- Given: Rectangle with length = 8 cm and breadth = 5 cm.
- Add length and breadth: \(8 + 5 = 13\) cm.
- Multiply by 2: \(2 \times 13 = 26\) cm.
- Final Answer: Perimeter = 26 cm
Units for Rectangle Perimeter
The perimeter of rectangle is always measured in the same unit as its length and breadth, such as centimeters (cm), meters (m), or inches (in). If length and breadth have different units, convert them to the same unit before calculating.
| Unit System | Perimeter Unit Example |
|---|---|
| Metric (SI) | cm, m, km |
| Imperial/US | in, ft, yd |
Why the Formula Is 2(l + b)
The formula \(2(l + b)\) for rectangle perimeter comes because opposite sides of a rectangle are always equal. So, the total length is length + breadth + length + breadth, which is simply twice the sum of length and breadth. This formula saves time and helps avoid mistakes in exams.
Solved Examples on Perimeter of Rectangle
Example 1: Find the perimeter of a rectangle with length 12 cm and breadth 7 cm.
1. Add the sides: \(12 + 7 = 19\) cm.2. Multiply by 2: \(2 \times 19 = 38\) cm.
Perimeter = 38 cm
Example 2: A rectangle has an area of 96 cm2, and the width is 4 cm less than the length. Find the perimeter.
1. Let length = x, width = x – 42. Area: \(x(x - 4) = 96\)
3. Solve: \(x^2 - 4x = 96 \Rightarrow x^2 - 4x - 96 = 0\)
4. Factor: \((x - 12)(x + 8) = 0\), so x = 12 (since length can’t be negative)
5. Width = 12 – 4 = 8 cm
6. Perimeter: \(2 \times (12 + 8) = 2 \times 20 = 40\) cm
Perimeter = 40 cm
Example 3: The perimeter of a rectangular room is 150 m. If the width is 10 m, what is the length?
1. Perimeter = 150 m, Width = 10 m2. Formula: \(2(l + b) = 150\)
3. \(l + 10 = 75\), so \(l = 65\) m
Length = 65 m
Perimeter vs Area of Rectangle
| Feature | Perimeter | Area |
|---|---|---|
| Meaning | Distance around rectangle | Surface covered inside |
| Formula | 2 (length + breadth) | length × breadth |
| Unit | cm, m, in, etc. | cm2, m2, in2, etc. |
Don’t confuse perimeter (boundary length) with area (space inside). You can quickly revise Area of Rectangle and Difference Between Area and Perimeter for more examples.
Speed Trick or Vedic Shortcut
Here’s a quick shortcut for the perimeter of rectangle: If both sides are the same (length = width), it’s a square! So perimeter = 4 × side.
Exam Tip: If one side is missing, just rearrange the formula: perimeter ÷ 2 – known side = unknown side.
Try These Yourself
- Find the perimeter of a rectangle with length 15 m and breadth 9 m.
- If the perimeter of a rectangle is 50 cm, and the length is 18 cm, what is the width?
- A rectangle has width half its length and perimeter 48 in. Find both side lengths.
- If length and breadth are given in meters and centimeters, convert to the same unit before applying the formula.
Frequent Errors and Misunderstandings
- Mixing up perimeter and area formulas.
- Forgetting to double the sum of sides (missing the "×2").
- Using wrong or mismatched units for length and width.
- Not adding units in the answer (cm, m, etc.).
Relation to Other Concepts
The idea of perimeter of rectangle connects closely with Area and Perimeter Formulas and Perimeter of Square. Mastering perimeter helps you solve more advanced questions on polygons and mensuration in later classes.
Classroom Tip
A quick way to remember the perimeter of rectangle formula: “P = 2 × (side + side)”, or think of wrapping a ribbon around a book—add both side lengths and multiply by 2. Vedantu’s teachers use fun analogies and live whiteboards so students build lifelong clarity.
We explored perimeter of rectangle—from definition, formula, and stepwise examples to exam tricks, frequent errors, and related concepts. Continue practicing with Vedantu and explore free resources for deeper mastery.
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FAQs on Perimeter of a Rectangle Explained for Students
1. What is the perimeter of a rectangle?
The perimeter of a rectangle is the total distance around its four sides. It's the sum of the lengths of all four sides. Because opposite sides of a rectangle are equal, we can calculate the perimeter using the formula: P = 2(l + b), where l represents the length and b represents the breadth (width) of the rectangle.
2. How do you calculate the perimeter of a rectangle?
To calculate the perimeter, follow these steps:
1. **Measure** the length (l) and breadth (b) of the rectangle.
2. **Add** the length and breadth: (l + b).
3. **Multiply** the sum by 2: 2(l + b).
The result is the perimeter of the rectangle. Remember to include the units (e.g., cm, m, inches) in your answer.
3. What is the difference between the perimeter and area of a rectangle?
The perimeter measures the distance around the rectangle, while the area measures the space inside the rectangle. The formula for area is A = l x b (length multiplied by breadth). Perimeter is measured in units of length (cm, m, etc.), while area is measured in square units (cm², m², etc.).
4. What are the units used for measuring the perimeter of a rectangle?
The units used for perimeter are units of length. Common units include centimeters (cm), meters (m), kilometers (km), inches (in), feet (ft), and yards (yd). The unit used depends on the size of the rectangle being measured.
5. How do I find the perimeter if only the area and one side of the rectangle are known?
If you know the area (A) and one side (let's say length, l), you can find the breadth (b) using the area formula: b = A/l. Once you have both length and breadth, you can use the perimeter formula: P = 2(l + b) to calculate the perimeter.
6. Can the perimeter of a rectangle ever be equal to its area?
Yes, it's possible. This happens when the specific dimensions of the rectangle satisfy both the perimeter and area equations simultaneously. For example, a rectangle with length 2 and breadth 1 has a perimeter of 6 units and an area of 2 square units; this is not an example of equality. Finding the exact dimensions where perimeter equals area would involve solving a quadratic equation.
7. How is the perimeter of a rectangle used in real-world situations?
The perimeter is used in many real-world applications, including:
• Determining the amount of fencing needed for a rectangular yard or field.
• Calculating the length of trim required for a rectangular picture frame.
• Measuring the amount of material needed to create a rectangular border or path.
• Finding the total distance covered in running around a rectangular track.
8. What if the rectangle is not aligned to a horizontal axis (i.e., it's tilted)?
Even if a rectangle is tilted, the perimeter calculation remains the same. The formula P = 2(l + b) still applies. The length and breadth are still the lengths of the opposite sides, regardless of the rectangle's orientation.
9. Why is the formula for the perimeter of a rectangle 2(l + b)?
The formula P = 2(l + b) arises because a rectangle has two pairs of equal sides. Adding the lengths of all four sides (l + b + l + b) simplifies to 2(l + b). This is a more efficient way to calculate the perimeter.
10. How do I solve word problems involving the perimeter of a rectangle?
To solve word problems, carefully read the problem to identify the given information (length, breadth, area, etc.). Write down what you know and what you need to find. Then, choose the appropriate formula (perimeter or area) and substitute the known values to solve for the unknown. Remember to always include the units in your final answer.
11. What if the sides of the rectangle are given in different units?
If the sides are given in different units (e.g., one side in meters and the other in centimeters), you must convert them to the same unit before calculating the perimeter. It's usually easiest to convert everything to the larger unit (meters in this case).
12. Are there any shortcuts or tricks to quickly calculate the perimeter?
The formula P = 2(l + b) is already quite efficient. However, if you're working with simple numbers, you can often mentally add the length and breadth and then double the sum. Practice will help you develop speed and accuracy in perimeter calculations.
