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
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