# 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

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

Questions and Answers 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?

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