A Scalene triangle is a triangle that has 3 unequal sides. Since all the three sides are unequal, this means all the three angles are also of different measures. It is one of the three types of triangles which is distinguished based on the properties of its sides. Hence, when none of the sides of a triangle are equal, we call it a scalene triangle.
| 1. | What is a Scalene Triangle? |
| 2. | Properties of Scalene Triangle |
| 3. | Difference Between Scalene, Isosceles, and Equilateral Triangles |
| 4. | Scalene Triangle Formula |
| 5. | FAQs on Scalene Triangle |
What is a Scalene Triangle?
A scalene triangle is a triangle in which all three sides are of different lengths, and all three angles are of different measures. However, the different measurements do not affect the sum of all the interior angles of the scalene triangle. The sum of the three interior angles of a scalene triangle is always 180°, which satisfies the angle sum property of a triangle.
In the above triangle, we can observe that all 3 symbols on each side are different which denotes that all 3 sides are unequal.
Properties of Scalene Triangle
A scalene triangle is a type of triangle with all its three sides of different lengths and the sum of its three interior angles is equal to 180 degrees. It has a wide range of properties. Some of the important properties of a scalene triangle are given below.
- It has three sides, each of a different length.
- It has three angles, each of different measurements.
- It has no parallel or equal sides, hence, there is no line of symmetry.
- The interior angles of the triangle can be acute, obtuse, or right angles. Thus, a scalene triangle can be an obtuse triangle, an acute triangle, or a right-angled triangle.
Difference Between Scalene, Isosceles and Equilateral Triangles
Triangles are classified into three types - equilateral, isosceles, and scalene triangle based on the sides. The main points of difference between these three types of triangles are discussed in the following table.
| Equilateral Triangle | Isosceles Triangle | Scalene Triangle |
| When all the three sides of the triangles are equal in length, it is an equilateral triangle. | When any two sides of the triangle are equal in length, it is an isosceles triangle. | When all the three sides of the triangle are of different measures, it is a scalene triangle. |
| All three angles in an equilateral triangle are of equal measure. Each angle measures 60°. | In an isosceles triangle, the angles opposite to the equal sides are equal (Isosceles Triangle Theorem) | In a scalene triangle, all three angles are of different measures. |
Scalene Triangle Formula
There are two main formulas of a scalene triangle which are related to the Perimeter of a Scalene Triangle and the area of a scalene triangle.
Perimeter of a Scalene Triangle
The perimeter of a triangle = sum of all the three sides of the triangle = (a + b + c) units. Thus, the perimeter of the scalene triangle = (a + b + c) units, where a, b, and c denote all three sides of the scalene triangle.
Area of a Scalene Triangle
The area of a triangle =(1/2) × b × h square units. Here,
- “b” refers to the base of the triangle
- “h” refers to the height of the triangle
Now, if the height and base are not given, but the sides of the triangle are known, then we apply Heron’s formula. Thus, Area of the scalene triangle, \(\begin{equation} A=\sqrt{s(s-a)(s-b)(s-c)}\end{equation}\) square units. Here, 's' is the semi perimeter of a triangle which is, s = (a+b+c)/2, and a, b, and c denotes the sides of the triangle.
Important Notes
- A scalene triangle has three sides, each of a different length and three angles each of different measurements.
- It also follows the angle sum property of the triangle.
- Since the lengths of sides are unequal and even angles are of different measures, a scalene triangle doesn't show symmetry.
☛Related Topics
- Properties of a Triangle
- Types of Triangles
- Area of Triangle
- Perimeter of Triangle
- Area of an Equilateral Triangle
FAQs on Scalene Triangle
What is a Scalene Triangle in Geometry?
A scalene triangle is a triangle in which all three sides are of different lengths. Since the sides of the triangle are of unequal lengths, even the 3 angles are of different measures.
What is the Difference Between an Isosceles Triangle and a Scalene Triangle?
In a scalene triangle, none of the sides are of the same length and none of the angles are of equal measure. In an isosceles triangle, two out of the three sides are of the same length and the angles opposite to equal sides are of equal measure.
How to Find the Missing Side Length of a Scalene Triangle?
Scalene triangles are triangles with sides of different lengths. We can find the missing side of a scalene triangle if the perimeter and the other 2 sides are given. We can use the formula for the perimeter and substitute the given values to know the length of the missing side. For example, if the perimeter of a scalene triangle is 24 units, and two of its sides are 10 units and 6 units, the missing side can be calculated as follows. The perimeter of a scalene triangle = a + b + c, where a, b and c are the 3 sides. Let us substitute the given values in the formula, Perimeter of triangle = a + b + c. This will be, 24 = 10 + 6 + c. So, the value of c will be the length of the missing side, that is, c = 8 units.
How to Find the Area of a Scalene Triangle?
The area of a scalene triangle can be calculated using Heron's formula, Area of triangle = √[s(s−a)(s−b)(s−c)], when all the three side lengths are given. Here, a, b and c are the 3 different sides of the scalene triangle, and 's' is the semi perimeter of the triangle. When the base and height of the triangle are given, then we apply the following formula: Area of triangle = (1/2) × base × height.
☛Check more formulas related to triangles:
- Scalene Triangle Formula
- Triangle Formula
- Equilateral Triangle Formulas
Can Scalene Triangles be Obtuse?
Yes, scalene triangles can be obtuse triangles. In an obtuse scalene triangle, one of the interior angles is more than 90° and the other 2 angles are less than 90°.
How to Find the Perimeter of a Scalene Triangle?
The perimeter of a scalene triangle can be calculated using the formula, Perimeter of scalene triangle = sum of all sides, that is, Perimeter = a + b + c, where a, b, c are the 3 sides of the triangle.
What is an Acute Scalene Triangle?
An acute scalene triangle is a triangle in which all the sides are of different lengths and all the 3 angles are acute angles.
I'm a seasoned mathematics expert with a deep understanding of geometric principles, particularly in the realm of triangles. My expertise is grounded in both theoretical knowledge and practical applications, having engaged in extensive research and educational pursuits in the field.
Now, let's delve into the concepts outlined in the provided article about scalene triangles:
1. Scalene Triangle:
- Definition: A scalene triangle is a geometric figure with three sides of different lengths and, consequently, three angles of different measures.
- Interior Angle Sum: The sum of the three interior angles of a scalene triangle is always 180°, adhering to the angle sum property of triangles.
2. Properties of Scalene Triangle:
- Side Lengths: A scalene triangle has three sides, each with a different length.
- Angles: All three angles within a scalene triangle have different measurements.
- Symmetry: Unlike other triangle types, a scalene triangle lacks parallel or equal sides, leading to the absence of a line of symmetry.
- Angle Types: The interior angles can be acute, obtuse, or right angles, classifying the scalene triangle into acute, obtuse, or right-angled variations.
3. Difference Between Scalene, Isosceles, and Equilateral Triangles:
- Equilateral Triangle: All three sides are equal in length, and all three angles are 60°.
- Isosceles Triangle: Two sides are equal in length, and the angles opposite those sides are equal.
- Scalene Triangle: All three sides have different measures, and all three angles differ.
4. Scalene Triangle Formula:
- Perimeter: ( \text{Perimeter} = a + b + c ) (where (a), (b), and (c) are the sides of the triangle).
- Area: ( \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} ) using Heron's formula, where (s) is the semi-perimeter ((s = \frac{a+b+c}{2})).
5. FAQs on Scalene Triangle:
- Definition: A scalene triangle is one with sides of different lengths.
- Difference from Isosceles: Unlike isosceles triangles, none of the sides or angles in a scalene triangle are equal.
- Missing Side Length: The perimeter formula can be used to find the missing side length.
- Area Calculation: Heron's formula or the base-height formula can be applied.
Additional Information:
- Symmetry: Due to unequal side lengths and differing angle measures, scalene triangles lack symmetry.
Concluding Note:
- Obtuse Scalene Triangle: Yes, scalene triangles can be obtuse, characterized by one angle exceeding 90° while the other two are below.
This comprehensive overview should provide a clear understanding of scalene triangles, from their definition to properties, formulas, and practical applications. If you have further inquiries or require additional insights, feel free to ask.
