## Perimeter of a Rectangle

Rectangles space four-sided polygons. Adhering to are the properties of a rectangle:

**(i)** every the angles of a rectangle space 90º.

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**(ii)** Opposite political parties of a rectangle are constantly the very same in size.

## Perimeter the a rectangle

The perimeter the a rectangle is the total length of every the political parties of the rectangle. Hence, us can discover the perimeter by adding all 4 sides that a rectangle.

Perimeter that the given rectangle is a + b + a + b. Because opposite political parties of a rectangle are always equal, we need to uncover the dimensions of only two political parties to uncover the perimeter the a rectangle.

The perimeter of the over rectangle with sides ‘a units’ and ‘b units’ is:

a + b + a + b = 2a + 2b = 2 (a + b) units.

Hence, the formula for the perimeter that a rectangle = 2 × (sum of adjacent sides)

**Examples of detect the perimeter of a rectangle**

**Example 1**. The 2 sides that the rectangle room given. What will certainly be the perimeter of the rectangle?

**Solution**: One side of the rectangle is 2 cm and the other side is 5 cm.

We know that, the perimeter that a rectangle = 2 × (sum of surrounding sides)

Therefore, the perimeter the the rectangle = 2 × (5 + 2) = 2 × (7) = 14 cm

**Example 2**. A rectangle-shaped playground is 20 m long and 13 m wide. Discover its perimeter.

**Solution**: One side of the rectangular playground is 20 m and also the various other side is 13 m.

We recognize that, the perimeter that a rectangle = 2 × (sum of nearby sides)

Therefore, the perimeter the the rectangular ground = 2 × (20 + 13) = 2 × (33) = 66 m

**Tricky difficulties involving perimeter that rectangles**

**Type I**: once the perimeter and also only among the sides are given.

**Example 1**. If the perimeter the the offered rectangle is 10 cm and the length of among its political parties is 2 cm. What will be the various other side?

**Solution**: The perimeter that the rectangle, with one of the sides equal to 2 cm, is 10 cm.

Let the lacking side be ‘a’.

We recognize that, the perimeter the a rectangle = 2 × (sum of adjacent sides)

10 = 2 × (2 + a) 5 = (2 + a)

a = 5 - 2 = 3 cm

**Type II**: finding sides using the properties of a rectangle.

Example 2. In the given rectangle, if a = 4 cm and also d = 3 cm. Find b and c.

**Solution**: We understand that next a = 4 cm and side d = 3 cm.

To uncover side b and c, we usage the property that the opposite political parties of a rectangle are constantly the exact same in size.

Hence, a = c = 4 cm and d = b = 3 cm.

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Many historical buildings have rectangle prefer shapes in castle e.g. Parthenon in Athens. |