A scalene triangle is a triangle in which all three sides have different lengths and all angles are diferent too.
This type of triangle can be a right triangle (one angle with measure 90°) but not all scalene triangles have a right angle. The scalene triangles can be acute (all interior angles measuring less than 90°), obtuse (one interior angle measuring more than 90°) or right triangles depending on their angles.
These three interior angles add to 180° (α+β+γ=180º) as in all of triangles.
It could also be calculated if a side (b) is known and the height (h) associated with that side.
If we know the length of the three sides you can calculate its perimeter using the following formula:
If only the length of two sides and the angle between them are given, in order to find the perimeter we need to calculate the other side using the Law of Cosines (Cosine Rule):
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.
Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.
Exercise of the Area of a Scalene Triangle
Find the area of the scalene triangle given its three sides: a=2 cm, b=4 cm and c=3 cm.
What is its area?
We can calculate the area using Heron’s formula. First, we have to determine the semiperimeter s:
Now, we can apply the Heron’s formula:
So, the area is 2.9 cm2.
Exercise of the Perimeter of a Scalene Triangle
Consider a given triangle:
Let be a scalene triangle of known sides, these being a=2 cm, b=4 cm y c=3 cm.
What is its perimeter? This will be calculated as the sum of its three sides.
So, the perimeter is 9 cm.
What is its perimeter?
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:
So, we get the side b=6.92 cm.
Now we can calculate the perimeter by adding the three sides of the triangle:
The perimeter of the triangle is 16.92 cm.
AUTHOR: Bernat Requena Serra