Session 3: Perimeter of Triangle – Formula, Definition, Interactives and Examples

What is Perimeter?

Perimeter is the distance around a shape. In other words, the total boundary length of a closed two-dimensional figure is called its perimeter. To find the perimeter of any two-dimensional shape, find the sum of the lengths of all the sides.

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Perimeter of Equilateral Triangle

An equilateral triangle has all three sides of the same length. The perimeter of an equilateral triangle is the sum of its three sides.

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Formula for Perimeter of Equilateral Triangle

Consider an equilateral triangle shown below. Let a denote the length of each equal side.

It follows from this formula that

Side of an equilateral triangle =\(\frac{1}{3}perimite{{r}_{equilateral triangle}}\)

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Perimeter of Isosceles Triangle

An isosceles triangle has two sides of the same length and the third side of different length. The perimeter of an isosceles triangle is the sum of its three sides. Since an isosceles triangle has two equal sides, the perimeter is twice the equal side plus the third (unequal) side.

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Formula for Perimeter of Isosceles Triangle

Consider an isosceles triangle shown below. Let a denote the length of each side and b  denote the length of the unequal side.

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Perimeter of Scalene Triangle

A scalene triangle has all three sides of different lengths. The perimeter of a scalene triangle is the sum of its three sides.

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Formula for Perimeter of Scalene Triangle

Consider a scalene triangle shown below. Let a, b and c denote the three sides of the scalene triangle.

\(\frac{Perimete{{r}_{scalene triangle}}}{2}\)=a+b+c

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Perimeter of Triangle – Examples

Example 1

Find the perimeter of an equilateral triangle with each side measuring 8 units.

We know,

Perimeter of an equilateral triangle=3×side

=3×8
=24 units

Example 2

Find the perimeter of the given scalene triangle.

We know,

The perimeter of a scalene triangle = Sum of all side lengths                                                  

Example 3

Each side of an equilateral triangle is 36 mm. Find the perimeter of the triangle. A square has its perimeter the same as that of the above triangle. Find the side length of the square.

We know,

The perimeter of equilateral triangle=3×side                                                    

Perimeter of square=4×side

Since the perimeter of the square is equal to the perimeter of the equilateral triangle, 

 The side of the square = 27 mm.

Example 4

A wire is bent in the form of a rectangle of length 25 cm and breadth 20 cm. If the same wire is bent in the form of an isosceles triangle having equal sides of length 25 cm, find the unequal side of the triangle.

Length of the wire = Perimeter of the rectangle                              

Now,

Length of the wire = Perimeter of the isosceles triangle       

Example 5

The cost of putting up a picket fence around an equilateral triangular farm at the rate of ₹220/m is ₹5280. Find the length of each side of the triangular farm.

The total cost of fencing the farm ₹=₹5280

Rate = ₹220/ m.

Cost = Perimeter× Rate

Perimeter=\(\frac{cost}{rate}\)               

We know,

Perimeter of an equilateral triangle=3×side

 24=3×side
side=\(\frac{24}{3}\)
=8 m

Therefore, the length of each side of the triangular farm = 8 m. 

• Perimeter is the total boundary length of a closed two-dimensional figure.
• The formula for the perimeter of an equilateral triangle is:
  Perimeter_{equilateral triangle}=3×side
• Using the formula for the perimeter of an equilateral triangle, we can find the side of the triangle: side=\(\frac{1}{3}\)Perimeter_{equilateral triangle}
• The formula for the perimeter of an isosceles triangle have two equal sides of length a and an unequal side of length b is:  
  Perimeter_{isosceles triangle}=2a+b
• The formula for the perimeter of a scalene triangle having sides a, b and c is: 
  Perimeter _{scalene triangle}=a+b+c