# Perimeter of Triangle

A three sided polygon which has three vertices and three angles is called a triangle. Equilateral triangle, Isosceles triangle and right angled triangle are the three different types of triangles. ΔABC represents a triangle with vertices or corners A, B, and C and side lengths a, b and c.

### How to calculate the perimeter of a triangle?

A Perimeter of the triangle is the total distance along the outside of the triangle.

Steps to calculate the Perimeter of a triangle:
• Note the lengths of all the sides of the triangle
• Add all the three lengths i.e, a+b+c
• Perimeter of a Triangle is given by a+b+c.

Note: The perimeter of an equilateral triangle is 3 times the length of each side as all the three sides are equal.

## Perimeter of a Triangle problems

Problem 1: A triangle sides measure 6 centimeters, 8 centimeters and 7 centimeters. What is its perimeter?

Solution: Length of  each side of triangle,

a = 6 cm

b = 8 cm

c = 7 cm

Perimeter of the Triangle = a+b+c=6+8+7= 21 cm.

Problem 2: Find the perimeter of an equilateral triangle with each side measuring 3 cm?

Solution: Length of  each side of an equilateral triangle, a = b = c = 3 cm

Perimeter of an equilateral triangle = 3*side length =3(3)=9

Thus the perimeter of given equilateral triangle is 9 cm.

Problem 3:  In a triangle two sides are 4 inches and 6 inches long. Its perimeter is 15 inches. Find the length of the third side.

Solution:  Given two sides of triangle, say a = 4 in and b = 6 in.

Let the third side be c inches.

The Perimeter of the triangle = 15 in. .......(1)

Also by the definition of Perimeter of triangle,

Perimeter of triangle = a+b+c=4+6+c  ...........(2)

Equating (1) and (2),

4+6+c=15

10+c=15

c=15-10 =5.

The third side is of length 5 inches.

Problem 4: Christy jogs around a triangular path which is equilateral in a park. If he jogs same distance every day and covers 36 kms in 6 days, what is the length of each side of the path?

Solution: The distance jogged by Christy in 6 days = 36 kms.

The distance jogged by Christy in 1 days = 36/6 = 6 kms.

Perimeter of the equilateral triangle path = The distance covered in a day

3 x length of each side of the path = 6 kms

Length of each side of the path = 6/3  = 2 kms

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