Perimeter of a Scalene Triangle

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Drawing of the scalene triangle

A scalene triangle is a triangle in which all three sides are in different lengths. The perimeter of a scalene triangle with three unequal sides is determined by adding the three sides.

If you know the length of the three sides, it’s easy to calculate its perimeter using the following formula:

Formula for the perimeter of a scalene triangle

If you know two sides of the triangle and the angle they form you can solve for the missing side using the Law of Cosines (Cosine Rule):

Formula for the perimeter of a scalene triangle knowing two sides and an angle

Download this calculator to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.

Triangle-total.rar         or   Triangle-total.exe      

Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.

Exercise 1

Consider a given triangle:

Exercise 1 of scalene triangle to calculate its perimeter

Let be a scalene triangle of known sides, these being a=2 cm, b=4 cm and c=3 cm.

What is its perimeter? This will be calculated as the sum of its three sides.

Calculating the perimeter of a scalene triangle

So, the perimeter is 9 cm.

Exercise 2

Drawing of exercise 2 of the perimeter

What is its perimeter?

Solution:

In this triangle we only know two sides (a=4 cm y c=6 cm) and the angle they form (B=85°). First we have to find the length of side b.

For this we use the Law of Cosines:

Calculation of side b in exercise 2

So, we get the side b=6.92 cm.

Now we can calculate the perimeter by adding the three sides of the triangle:

Result in exercise 2

The perimeter of the triangle is 16.92 cm.


AUTHOR: Bernat Requena Serra

YEAR: 2020


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