Perimeter of a Rectangle

# Perimeter of a Rectangle

## Perimeter of a Rectangle

We know that a rectangle is a plane figure or two-dimensional figure. The opposite sides of a rectangle are equal and all the angles of a rectangle are 90°.

The perimeter of a closed two-dimensional figure is the length of its boundary. The units of measurement of perimeter are the same as that of length, i.e. cm, m or km.

To find the perimeter of a rectangle, we add the measures of all its sides.

Let we have to find the perimeter of a given rectangle ABCD.

Perimeter of rectangle ABCD = AB + BC + CD + DA

= AB + BC + AB + BC           (Since, AB = CD and BC = DA)

= 2 AB + 2 BC

= 2 (AB + BC)

Thus, the perimeter of a rectangle = 2 (length + breadth)

## Perimeter of a Rectangle Formula

Perimeter of a rectangle = 2 (length + breadth)

## Perimeter of a Rectangle Example

Example 1: Find the perimeter of a rectangle whose length and the breadth measure

10 cm and 8.5 cm, respectively.

Solution: Given: l = 10 cm and b = 8.5 cm

Perimeter of a rectangle = 2 (l + b)

= 2 (10 + 8.5) cm

= 2 (18.5) cm

= 37 cm

Example 2: A rectangular plot is 80 m long and 60 m wide. Find the length of the

rope required to fence all around it.

Solution: Given: length of the plot, l = 80 m and breadth of the plot, b = 60 m

Perimeter of a rectangular plot = 2 (length + breadth)

= 2 (80 + 60) m

= 2 × 140 = 280 m

Hence, the total length of the rope required to fence the plot is 280 m.

Example 3: An athlete takes 40 rounds of a rectangular park which is 100 m long and 75 m wide. Find the total distance covered by the athlete in km.

Solution: Given: length of the park = 100 m and breadth of the park = 75 m

Distance covered by the athlete in 1 round = Perimeter of the park

= 2 (100 m + 75 m)

= 2 × 175 m = 350 m

Total distance covered by the athlete in 40 rounds = 40 × 350 m = 14000 m

Thus, the total distance covered in kilometres = 14000/1000 km

(Since, 1 km = 1000 m)

= 14 km

Example 4: If the perimeter of a rectangle is 550 cm and its breadth is 125 cm, find the length of the rectangle.

Solution: Given: perimeter of the rectangle = 550 cm and breadth of the rectangle = 125 cm

We know that,

Perimeter of a rectangle = 2 (l + b)

550 cm = 2 (l + 125)

l + 125 = 275

l = 150 cm

Hence, the length of the rectangle is 150 cm.

Example 5: The rectangular frame of a picture is 50 cm long and 40 cm wide. If the

border is 5 cm wide, then find the perimeter of the picture.

Solution: Given: Length of the frame = 50 cm

Length of the picture = 50 cm – (5 cm + 5 cm) = 40 cm

Width of the frame = 40 cm

Width of the picture = 40 cm – (5 cm + 5 cm) = 30 cm

Thus, the perimeter of the picture = 2 (length + breadth)

= 2 (40 cm + 30 cm)

= 2 × 70 cm = 140 cm

Hence, the perimeter of the picture is 140 cm.