**Perimeter of a Triangle**

We know that a triangle is a plane
figure or two-dimensional figure. A triangle has three sides and three vertices.
It has no diagonals. A triangle is a polygon with the least number of sides.

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 triangle,
we add the measures of all its sides.

Let us understand about the types of triangles according to its
sides and find their perimeter.

According to the sides, triangles are of three types.

1.
Scalene triangle

2.
Isosceles triangle

3.
Equilateral triangle

**Perimeter of a Scalene Triangle**

A triangle whose all the sides are of different measures is called
a **scalene triangle**.

Let the given triangle ABC is a scalene triangle. To find the perimeter
of triangle ABC, we add the measures of all its sides.

Thus, perimeter of the triangle = AB + BC + CA

If the measures of three sides of
a triangle are a, b and c, then

Perimeter of the scalene triangle
= a + b + c

Thus, the **perimeter of a
scalene triangle = a + b + c**

**Perimeter of an Isosceles Triangle**

A triangle whose two sides are of equal length is called an **isosceles
triangle**.

Let the given triangle ABC is an isosceles triangle. To find the perimeter
of triangle ABC, we add the measures of all its sides.

Thus, perimeter of the triangle = AB + BC + CA

Let AB = AC = a and BC = b, then

Perimeter of the isosceles triangle
= a + b + a

Thus, the **perimeter of an
isosceles triangle = 2a + b**

**Perimeter of an Equilateral Triangle**

A triangle whose all the three sides are of equal length is called
an** equilateral triangle**.

Let the given triangle ABC is an equilateral triangle. To find the
perimeter of triangle ABC, we add the measures of all its sides.

Thus, perimeter of the triangle = AB + BC + CA

Let AB = BC = CA = a, then

Perimeter of the equilateral triangle
= a + a + a

Thus, the **perimeter of an
equilateral triangle = 3a**

**Perimeter of a Right-angled Triangle**

A triangle whose one angle measures 90°, is called a **right-angled
triangle**.

Let the given triangle ABC is a right-angled triangle. To find the
perimeter of triangle ABC, we add the measures of all its sides.

If only two sides of a right-angled triangle are given, we can calculate the third side of the triangle using Pythagoras Theorem.

Pythagoras theorem states that, AC^{2} = AB^{2} +
BC^{2}

After finding the length of the third side, we can find the
perimeter of the triangle.

Perimeter of the triangle = AB + BC + CA

Thus, the **perimeter of a right-angled
triangle = a + b + c**

Where a, b and c are the three sides
of the right-angled triangle.

**Perimeter of a Triangle
Example**

**Example 1: **Find
the perimeter of a triangle whose three sides measure 7.5 cm, 8 cm, and 6.5 cm.

**Solution: **Given:
a = 7.5 cm, b = 8 cm and c = 6.5

Perimeter of a triangle = a + b +
c

= 7.5 + 8 + 6.5

= 22 cm

**Example 2: **A
traffic sign board is in the shape of an equilateral triangle. If each side of
the board measures 90 cm, find the perimeter of the board.

**Solution: **Given:
each side of the board, a = 90 cm

Perimeter of an equilateral triangle =
3a

= 3 × 90 cm

= 270 m

Hence, the perimeter of the sign board
is 270 m.

**Example 3: **If the base and the perimeter of an isosceles triangle are 7 cm
and 23 cm, respectively, find the measure of the equal sides.

**Solution: **Given: base, b = 7 cm, perimeter = 23 cm

Perimeter of an isosceles
triangle = 2a + b

23 = 2a + 7

2a = 16

a = 8

Hence, the measures of equal
sides are 8 cm.

**Example 4: **The base and the perpendicular of a right-angled triangle are 5
cm and 12 cm. Find the perimeter of the triangle.

**Solution: **Given: base = 5 cm and perpendicular
= 12 cm

(Hypotenuse)^{2}
= (base)^{2} + (perpendicular)^{2}

(Hypotenuse)^{2}
= (5)^{2} + (12)^{2}

(Hypotenuse)^{2}
= 25 + 144 = 169

Hypotenuse = 13

Perimeter of the
right-angled triangle = a + b + c

= 5 + 12 + 13

= 30
cm

Hence, the perimeter of
the right-angled triangle is 30 cm.

**Example 5: **Rashmi
walks 10 rounds of a park daily. If the park is in the shape of an equilateral
triangle and she walks 1.5 km daily, find the length of each side of the park.

**Solution: **Given:
distance covered in 10 rounds = 1.5 km = 1.5 × 1000 m = 1500 m

Distance covered in 1 round = 1500/10
= 150 m

Therefore, the perimeter of the park =
150 m

3a = 150

a = 150/3 = 50 m

a = 50 m

Hence, each side of the park measures 50 m.