Theory:

Now, we shall find the perimeter of a triangle.
 
perimeter-w300.png
 
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.
 
Cdfd-w300.png
 
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 \(27 \ cm\).