### Theory:

Now, we shall find the perimeter of a triangle.

Let $$ABC$$ be a triangle with sides of length $$a$$, $$b$$ and $$c$$ $$units$$.

Then, the perimeter of the triangle $$ABC$$ is given by:
Perimeter of the triangle $$=$$ Sum of the measures of all three sides
Perimeter $$P = AB+BC+CA$$ $$units$$

$$P = a+c+b$$ $$units$$

Therefore, the perimeter of the triangle is $$P = a+b+c$$ $$units$$.
Example:
1. The sides of the triangle are $$7 \ cm$$, $$8 \ cm$$ and $$10 \ cm$$. Find the perimeter of the triangle.

Solution:

Let $$a$$, $$b$$ and $$c$$ denote the sides of the triangle. Then, $$a = 7 \ cm$$, $$b = 8 \ cm$$ and $$c = 10 \ cm$$.

Perimeter of the triangle $$=$$ Sum of the measures of all three sides

Substituting the values in the formula, we have:

Perimeter, $$P = a+b+c$$

$$P = 7+8+10$$ $$cm$$

$$P = 25 \ cm$$

Thus, the perimeter of the triangle is $$25 \ cm$$.
Let us find the perimeter of an equilateral triangle.
A triangle in which all three sides were in the equal length is called the equilateral triangle.

Let $$ABC$$ be an equilateral triangle which has sides of length $$a$$ units.

We know that the formula to find the perimeter of the triangle is $$P = a+b+c$$, where $$a$$, $$b$$, $$c$$ are the lengths of three sides of the triangle.

Since for an equilateral triangle, all the sides were equal, then substituting $$a = b = c = s$$ in the formula of the perimeter of the triangle, we have:

Perimeter, $$P = s+s+s$$ $$units$$

Therefore, the perimeter of the equilateral triangle is $$P = 3s$$, where $$s$$ is the length of three equal sides.
Example:
1. The side length of an equilateral triangle is $$9 \ cm$$. Find the perimeter of an equilateral triangle.

Solution:

The side length of an equilateral triangle is $$s = 9$$ $$cm$$.

Perimeter $$= 3s$$, where $$s$$ is the length of three equal sides.

Substituting the value of $$s$$ in the above formula, we have:

Perimeter $$= 3 \times 9$$ $$cm$$

Perimeter $$= 27$$ $$cm$$

Therefore, the perimeter of an equilateral triangle is $$27 \ cm$$.