The perimeter of a triangle, in simple terms, is just a measure for the total length around the triangle.

Definition

The perimeter of a triangle: the sum of the lengths of the triangle's three sides.

The quantity is a linear one and gives the length of the boundary of the triangle.

Mathematical Context:

Types of Triangles: The perimeter formula applies to all kinds of triangles, including scalene, where all sides are different; isosceles, where two sides are equal; or equilateral, where all sides are equal.

Units: Perimeter units are the same as those for the sides of a triangle—such as meters, centimeters, or inches.

Derivation

For a triangle to exist, certain conditions need to be met. For any triangle having sides a, b, c, one of the following three conditions must be true.

a + b > c

b + c > a

c + a > b

The formula for Perimeter of a Triangle is

P = a+b+c

Solved examples

Question 1: Find the perimeter of a triangle whose sides are 6 cm, 8 cm and 10 cm.

Solution:

Given,

a = 6 cm

b = 8 cm

c =  10 cm

Perimeter of a Triangle = a + b + c

= 6 + 8 + 10

= 24 cm

Question 2: Find the perimeter of an equilateral triangle whose side is  6 cm.

Solution:

Since it is an equilateral triangle, all the sides are equal.

Thus, a = 7

Perimeter of an equilateral triangle= a + b + c = a + a + a = 3a

= 3 x a

= 3 x 7

= 21 cm

Question 3: Find the perimeter of an isosceles triangle whose equal sides measure 8 cm and the third side is 12 cm.

Solution:

Being an isosceles triangle, two sides are equal.

Thus, a = 8, b = 8 and c = 12

Perimeter of an isosceles triangle= a +b + c = a + a + c = 2a + c

=2 x 8 + 12

= 16 + 12

= 28 cm

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