**Perimeter of Rectangle**

**What is Perimeter?**

Perimeter is defined as the total length around a closed figure. The total sum of the lengths of the sides of a closed geometrical shape gives us its perimeter.

In a rectangle, opposite sides are equal in length, so the formula to calculate the perimeter is:

Consider a rectangle with length ‘L’ and breadth ‘B’ as shown in the figure.

Perimeter = L + B + L + B

Perimeter = 2L + 2B

Therefore, the perimeter of the rectangle = 2(L + B)

To find the perimeter of a rectangle, you need to know the values of its length and width. Once you have those values, you can substitute them into the formula and calculate the perimeter.

For example, let’s say we have a rectangle with a length of 5 units and a width of 3 units. Using the formula, we can find the perimeter as follows:

Perimeter = 2 × (5 + 3)

Perimeter = 2 × 8

Perimeter = 16 units

Therefore, the perimeter of a rectangle with a length of 5 units and a width of 3 units is 16 units.

The perimeter of a rectangle is typically measured in the same unit as the side lengths. It represents the total distance around the outside of the rectangle and is useful in various applications such as construction, landscaping, and geometry.

**Solved Examples on Perimeter of Rectangle:**

**Example 1:** Find the perimeter of a rectangle with a length of units and a width of 4 units.

Solution:

Using the formula: Perimeter = 2 × (Length + Width)

Substituting the given values:

Perimeter = 2 × (6 + 4)

Perimeter = 2 × 10

Perimeter = 20 units

Therefore, the perimeter of the rectangle is 20 units.

**Example 2:** The perimeter of a rectangle is 36 meters, and its length is 10 meters. Find the width of the rectangle.

Solution:

Using the formula: Perimeter = 2 × (Length + Width)

Substituting the given values and letting the width be “w”:

36 = 2 × (10 + w)

36 = 20 + 2w

2w = 36 – 20

2w = 16

w = 8

Therefore, the width of the rectangle is 8 meters.

**Example 3:** The perimeter of a rectangle is 52 centimetres, and its width is 12 centimetres. Find the length of the rectangle.

Solution:

Using the formula: Perimeter = 2 × (Length + Width)

Substituting the given values and letting the length be “l”:

52 = 2 × (l + 12)

52 = 2l + 24

2l = 52 – 24

2l = 28

l = 14

Therefore, the length of the rectangle is 14 centimetres.

**Frequently Asked Questions on Perimeter of Rectangle:**

1: What is the perimeter of a rectangle?

Answer: The perimeter of a rectangle is the total distance around its outer boundary. It is the sum of all the side lengths.

2: How do you calculate the perimeter of a rectangle?

Answer: To calculate the perimeter of a rectangle, you can use the formula: Perimeter = 2 × (Length + Width). This formula adds up the length of all the sides.

3: Do all sides of a rectangle have the same length?

Answer: No, a rectangle has two pairs of equal-length sides, but the lengths of the pairs may differ from each other. The opposite sides of a rectangle are equal in length.

4: Can the perimeter of a rectangle be zero?

Answer: No, the perimeter of a rectangle cannot be zero. A rectangle must have positive non-zero lengths for its sides in order to enclose an area.

5: What units are used to measure the perimeter of a rectangle?

Answer: The units used to measure the perimeter of a rectangle are the same as the units used for the side lengths. For example, if the sides are measured in meters, the perimeter will be in meters.

6: Can the perimeter of a rectangle be negative?

Answer: No, the perimeter of a rectangle cannot be negative. Perimeter is a measure of distance, and distance cannot be negative.

7: Can the perimeter of a rectangle be larger than the sum of its side lengths?

Answer: No, the perimeter of a rectangle cannot be larger than the sum of its side lengths. The perimeter is the sum of all the sides, so it cannot exceed the sum of those lengths.

8: Why is the perimeter of a rectangle useful?

Answer: The perimeter of a rectangle is useful in various applications, such as calculating the amount of fencing needed for a rectangular area, determining the distance around a rectangular track or field, or finding the total length of borders or boundaries in geometric problems.