**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)

= 2 (length + breadth)

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.