# Perimeter of a Triangle

We will discuss here how to find the perimeter of a triangle. We know perimeter of a triangle is the total length (distance) of the boundary of a triangle.

Perimeter of a triangle is the sum of lengths of its three sides.

For example, perimeter of the ∆PQR = PQ + QR + RP

The perimeter of a triangle ABC

= AB + BC + CA

= 2 cm + 4 cm + 3 cm,

(add the length of each side of the triangle).

= 9 cm

Perimeter of the triangle = Sum of the sides.

● A triangle has 3 sides

The perimeter of the triangle XYZ

= 3 cm + 5 cm + 4 cm

= 12 cm

The perimeter of the triangle = Sum of the lengths of three sides.

Let us consider some of the examples on perimeter of a triangle:

1. Find the perimeter of a triangle having sides 3 cm, 8 cm and 6 cm.

Solution:

Perimeter of a triangle

= Sum of all the three sides

= AB + BC + AC

= 3 cm + 8 cm + 6 cm

= 17 cm

2. Find the perimeter of the triangle PQR whose sides are 4 cm, 6 cm and 8 cm.

Solution:

In the figure PQ = 4 cm, PR = 6 cm and QR = 8 cm

The perimeter of the rectangle PQR

= 4 cm + 6 cm + 8 cm

= 18 cm

3. Find the perimeter of an equilateral triangle whose one side is 5 cm.

Solution:

A triangle in which all the sides are equal is called an equilateral triangle.

Perimeter of the equilateral triangle = 3 × side

= 3 × 5 cm

= 15 cm

Thus, perimeter = 15 cm.

4. Find the perimeter of a triangle whose length of three sides are 8 cm, 11 cm, 13 cm.

Solution:

To find the perimeter of the triangle, we add all the sides together.

Perimeter of a triangle

= Sum of all the three sides

= 8 cm + 11 cm + 13 cm

= 32 cm

5. Find the perimeter of a triangle whose sides are 5 cm, 2 cm and 3 cm.

Solution:

Perimeter of the triangle is the sum of the lengths of its sides.

Perimeter = 5 cm + 2 cm + 3 cm

Thus, perimeter = 10 cm.

6. Find the perimeter of each triangle.

Solution:

(i) Perimeter of ∆XYZ = 5.5 cm + 6 cm + 6 cm = 17.5 cm

(ii) Perimeter of ∆ABC = 8 cm + 6 cm + 6 cm = 20 cm

(iii) Perimeter of ∆PQR = 4 cm + 3 cm + 5 cm = 12 cm

7. Find the perimeter of the given shapes.

Solution:

(i) Perimeter = PQ + QR + RS + ST + TU + UV + VP

= 2.5 cm + 3 cm + 2 cm + 3 cm + 2.5 cm + 4 cm + 4 cm

= 21 cm

(ii) Perimeter = PQ + QR + RS + SP

= 4 cm + 4 cm + 4 cm + 4 cm

= 16 cm

(iii) Perimeter = PQ + QR + RS + ST + TP

= 7 cm + 6 cm + 4 cm + 3 cm + 5 cm

= 25 cm

8. How to find the perimeter of a triangle?

Find the perimeter of the given triangle.

Solution:

To find the perimeter of a triangle, we measure the three sides of the triangle and add them together.

In the above given figure,

AB = 4 cm

BC = 8 cm and

AC = 7 cm.

Therefore, perimeter of the triangle = 4 cm + 8 cm + 7 cm

= 19 cm

Word Problems on Perimeter of a Triangle:

1. Two sides of a triangle are 3 cm and 4 cm. Find the third side of the triangle if its perimeter is 11 cm.

Solution:

First side of the triangle                            = 3 cm

Second side of the triangle                        = 4 cm

Perimeter of the triangle                           = Sum of the lengths of sides

i.e. sum of the lengths of the sides            = 11 cm

3 cm + 4 cm + length of the third side      = 11 cm

7 cm + length of the third side                 = 11 cm

But we know that 7 cm + 4 cm                = 11 cm (Note: 11 – 7 = 4)

Therefore, length of the third side            = 4 cm

Worksheet on Perimeter of a Triangle:

1. A triangle has a perimeter of 50 cm. If its two sides are of lengths 15 cm and 19 cm, what is the length of the third side?

2. Find the perimeter of each of the following triangles:

2. (i) Perimeter of the triangle 12 cm.

(ii) Perimeter of the triangle 15 cm.

(iii) Perimeter of the triangle 18 cm.

(iv) Perimeter of the triangle 15 cm.

3. Finding missing side length of the triangle when perimeter is given:

3. 5 cm

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