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Perimeter of Triangle

Last Updated : 08 May, 2024
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Perimeter of Triangle is the total length of all its three sides. A triangle is a polygon that has three sides or edges, three vertices, as well as three angles, hence the name triangle. The triangle is the most fundamental closed polygon in geometry, as it is the first possible closed polygon. With only two vertices, we can only form a line, not any closed polygon. Additionally, we can divide any polygon into triangles. For example, we can divide a quadrilateral using its diagonal into two triangles, a pentagon using two diagonals from the same vertex into three triangles, and so on.

In this article, we have provided all the important details related to like its definition, the formula for perimeter of triangle, and how to find the perimeter of triangle.

What is the Perimeter of Triangle?

Perimeter of triangle is the total distance covered along the boundary of any triangle. In other words, a measure of all the edges is the perimeter of a triangle. Generally, the perimeter is the same for all the geometric 2-D shapes which is the total length of the boundary of the figure. As perimeter is the measure of length, it is measured in meters, centimeters, kilometers, etc.

Perimeter of Triangle Definition

Perimeter of a triangle is the total length of the outer boundary or the sum of the lengths of its three sides.

P = side1 + side2 + side3

Real-Life Examples on Perimeter of Triangle

The perimeter of a triangle is used to calculate the length of wire used to fence any triangular field. It is also used to build triangular furniture, table, and other objects.

Real-Life Example of use of Perimeter of Triangle:

Perimeter of Triangle Formula

For finding the perimeter of a triangle sum of the length of all its sides is taken. The formula required to find the perimeter of a triangle is:

Perimeter = Sum of the Three Sides of a Triangle

Let us understand this formula with the different types of triangles.

Perimeter of a Scalene Triangle

The perimeter of a triangle is equal to the sum of all sides of a triangle. Any triangle with three unequal sides is known as Scalene Triangle. If the sides of a triangle have lengths equal to a, b, and c, then,

Perimeter of a Scalene Triangle

Perimeter of an Isosceles Triangle

For an isosceles triangle, i.e., any triangle with two sides equal, let two equal sides are of length ‘b‘ units and the length of the unequal side equals ‘c‘, then, 

Perimeter of an Isosceles Triangle

Perimeter of an Equilateral Triangle

For an equilateral triangle, since all sides are equal in length, thus a = b = c. Hence,

Perimeter of an Equilateral Triangle

Check: Isosceles right triangle

Perimeter of a Right Triangle

For a right-angle triangle i.e. the triangle with one angle of 90°. The perimeter is calculated by adding the length of all given sides. Formula to find the perimeter of a right triangle is:

Perimeter of a Right Triangle

where, 

a is the perpendicular, b is the base and c is the hypotenous of the right-angled triangle.

Check: Pythagoras theorem

How to Find the Perimeter of Triangle

Perimeter of a triangle is calculated using the steps discussed below:

Step 1: Mark the measurement of each side of the triangle and make sure all the measurements are in the same unit.
Step 2: Add the value of all the sides to find the perimeter.
Step 3: The sum obtained in step 2 is the required perimeter(use unit same as the length of sides.)

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Perimeter of a Triangle Examples

Example 1: If the length of the sides of a triangle is 4cm, 5cm, and 6cm, then what is the perimeter of the triangle?

Solution:

Given, the sides of the triangle are 4cm, 5cm, and 6cm. Thus, it is an scalene triangle.

So the perimeter of the triangle  = Sum of sides = 4 + 5 + 6 = 15cm

Example 2: In an isosceles triangle, the two sides are given as 5cm and 6cm. What can be the perimeter of the triangle?

Solution:

Given, the triangle is the isosceles triangle. Thus, any two sides of the triangle are equal.

So, the third side can be either 5cm or 6cm.

If the third side is 5cm, then,

Perimeter = 5 + 5 + 6 = 16cm

If the third side is 6cm, then,

Perimeter = 5 + 6 + 6 = 17cm

So, the perimeter can be either 16cm or 17cm.

Example 3: What is the perimeter of an equilateral triangle whose one side length is 5cm?

Solution:

Given that the triangle is an equilateral triangle, thus all three sides are equal in length.

Since one side is equal to 5cm, the other two sides will also be equal to 5cm.

So, Perimeter = 5 + 5 + 5 = 15cm.

Example 4: Given the perimeter of an equilateral triangle is 21cm, find the length of its three sides.

Solution:

Since, in an equilateral triangle, all the three sides are equal in length, the perimeter is equal to three times the length of a side.

Let’s the length of any side be equal to ‘a’ units. So perimeter is equal to ‘3a’ units.

So, we can write,

3a = 21

a = 7cm

Thus, the length of each side is equal to 7cm.

Example 5: Find the length of two equal sides of an isosceles triangle if the length of the unequal side is 5cm and the perimeter is 17cm.

Solution:

Given, the length of unequal side is 5cm and perimeter is 17cm.

Since, it is isosceles triangle, length of other two sides are equal. Let each equal side length be ‘a’ units.

Thus, perimeter = a + a + 5

Since, perimeter = 17cm, we can write,

17 = a + a + 5

2a + 5 = 17

2a = 12

a = 6cm

Thus, the length of the equal sides of the isosceles triangle is 6cm.

Practice Questions on Perimeter of Triangle

Q1: What is the Perimeter of an Isosceles Triangle having equal sides 20 cm and uneqal side 13 cm.

Q2: Find the length of the side of an Equilateral Triangle whose perimeter is 27 cm.

Q3: John cycles along the boundary of a traingle park whose dimensions are given as 10 cm, 12 cm and 20 cm. Find the distance covered by John.

Q4: Find the semiperimeter of a Triangle of sides 3 cm, 4 cm and 5 cm.

Perimeter of Triangle – FAQs

What is the Formula for the Perimeter of an Equilateral Triangle?

For an Equilateral Triangle, all sides are equal. Thus, perimeter of an equilateral triangle is = 3a units, where a is the length of side of a triangle.

What is the Perimeter of Triangle in math?

Perimeter of a triangle is the total length of the sides of a triangle. If a, b, and c are the sides of a triangle then perimeter = a + b + c.

What is the Perimeter of an Equilateral Triangle?

Perimeter of a triangle is the length of all its sides. In an equilateral triangle with side a. Perimeter = 3×a

How do we find the Perimeter of Triangle?

To calculate the perimeter of the triangle sum of all its three sides are added.

How many Triangles with a Perimeter of 8 units?

Only one triangle is possible with perimeter 8 and its side are of length 8/3, 8/3, and 8/3 units.

What is the Formula for the perimeter of isosceles triangle?

Isosceles triangle has 2 equal sides. so, the formula for the perimeter of an isosceles triangle is given as

P = 2a + b units, where ‘a’ is the measure of equal sides of a triangle and ‘b’ is the third side.

Can a Triangle Have the Same Area and Perimeter?

Yes, A triangle can have equal area and perimeter and the triangle with equal perimeter and area is called an equable triangle.



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