Perimeter of a Triangle

Topic

Triangles

Definition

The perimeter of a triangle is the sum of the lengths of its three sides.

Description

The perimeter of a triangle is a fundamental concept in geometry, representing the total distance around the triangle. The perimeter is calculated by adding the lengths of the triangle's three sides.

This concept is essential in various real-world applications, such as in land measurement, construction, and design. For example, calculating the perimeter of a triangular plot of land helps in land valuation and planning. In construction, understanding the perimeter is crucial for determining the amount of materials needed for a project.

In math education, learning how to calculate the perimeter of a triangle helps students understand the broader concepts of measurement and geometry. It also provides a foundation for more advanced topics, such as trigonometry and calculus. By mastering this concept, students can apply their knowledge to solve practical problems and develop a deeper understanding of geometric principles.

For a complete collection of terms related to functions and relations click on this link: Triangles Collection

The following section includes background information on the general topic of perimeter and specifically on the perimeter of a triangle.

Brief Review of Triangle Perimeter

Watch this video to learn about triangle perimeter. (The video transcript is also available.)

Brief Review of Perimeter

The perimeter of a geometric shape is the distance around it.

For now, let's just look at the perimeter of a polygon. Take a look at this polygon and make a note of the measurements of the side lengths.

Simply add the side lengths to find the perimeter:

P = 3 + 2 + 3 + 6 + 4

= 17

Perimeter of a Triangle

A triangle is a type of polygon. It has three sides. The perimeter of a triangle is the sum of the lengths of the three sides. Here’s an example.

Simply add the side lengths to find the perimeter:

P = 3 + 6 + 4

= 13

Sometimes a triangle has side lengths that are variables. Take a look at this triangle.

Simply add the side lengths to find the perimeter:

Perimeters of Special Triangles

Finding the perimeter with certain types of triangles can be easier. For example, consider an isosceles triangle. 

Notice that two of the sides have the same length. Here’s how to calculate the perimeter of an isosceles triangle:

Perimeter = 2•7 + 5

= 14 + 5

= 19

An equilateral triangle has three equal sides. Look at the following equilateral triangle. Notice that the perimeter is simply 3 times the length of one of the sides.

P = 3 • 9

= 27

Right triangles have two legs and a hypotenuse. Because of the Pythagorean Theorem, there is a relationship between the legs and sides. Use that to find the perimeter of the triangle, as shown below.

Perimeters of Similar Triangles

When two triangles are similar, their sides are proportional. How does this affect the perimeter? Take at look at these two similar triangle:

 Notice that corresponding sides are in a 2:1 ratio. For example, the base of the smaller triangle is 3 and the base of the larger triangle is twice that. The same ratio holds for the other two corresponding sides. How does this affect the perimeters? This table shows the perimeter calculators for each triangle:

Notice that the perimeters are also in the 2:1 ratio.

Solving Perimeter Equations

There are cases where you know the perimeter and need to find the side length. For example, here is a triangle-shaped garden. It is the in the shape of an isosceles triangle with a perimeter of 50 ft. How can you use the information provided to find the side lengths labeled x.

We know that the perimeter of an isosceles triangle has this equation. The 2x term results from the fact that two of the sides of an isosceles triangle are congruent.

P = 2x + 10

Simply plug in the value for the perimeter and solve for x:

50 = 2x + 10

2x = 40

x = 20