# Obtuse Scalene Triangle: Definition with Examples

## What Is an Obtuse Scalene Triangle?

An obtuse scalene triangle is a triangle characterized by one obtuse angle (angle between 90 degrees and 180 degrees) and three sides of different lengths. These triangles are both scalene and obtuse.

Triangles can be classified on the basis of side-lengths and angle measurements.

An Obtuse Scalene Triangle is a type of a triangle based on both sides and angles. It has all the properties of an obtuse triangle and a scalene triangle.

• Obtuse triangle: It is a triangle that has one obtuse angle, and two acute angles. So, how does an obtuse angle look like? Take a look!
• Scalene triangle: It is a triangle where all three sides are of different lengths.

Obtuse Scalene Triangle Example:

In the given triangle, the angle A is an obtuse angle. The remaining two angles are acute. All three sides have different lengths. It is an obtuse scalene triangle.

## Obtuse Scalene Triangle: Definition

An obtuse scalene triangle is a triangle that has three sides of different measurements and one interior angle that is obtuse (between 90° and 180°).

## Properties of an Obtuse Scalene Triangle

As mentioned earlier, an obtuse scalene triangle has the properties of both scalene and obtuse triangle

• There are two acute angles (less than 90°) and one obtuse angle (between 90° and 180°).
• All the sides of an obtuse scalene triangle are of different lengths.
• All angles of an obtuse scalene triangle are different in measure.
• The side opposite to the obtuse angle is the longest side.
• The sum of all three interior angles of the obtuse scalene triangle is 180°.

## Obtuse Scalene Triangle Formulas

Let’s discuss the formulas to find the area and perimeter of a scalene obtuse triangle.

Perimeter of an obtuse scalene triangle

The perimeter of an obtuse scalene triangle is the sum of the three sides. It is the total length of its outer boundary. Perimeter is measured in linear units such as inches, feet, etc.

P = (a + b + c)

where

a, b, and c are the lengths of the sides of the triangle.

Area of an obtuse scalene triangle area

Area of an obtuse scalene triangle is the total region covered within its boundary. Let’s understand how to find the area of an obtuse scalene triangle.

• Area using base and height:

Area $= \frac{1}{2} \times b \times h$

where

b is the base

h is the height of the triangle.

Note: The height of an obtuse angled triangle drawn will lie outside the triangle.

• Area using side-lengths

If all the sides of the scalene obtuse triangle are given, then the area of an obtuse scalene triangle can be calculated using Heron’s formula.

Area $= \sqrt{s(s – a)(s – b)(s – c)}$

where

s denotes the semi perimeter and $s = \frac{(a + b + c)}{2}$

a, b, and c are the sides of the given triangle.

## Facts about Obtuse Scalene Triangle

• A scalene triangle can be an obtuse-angled triangle, acute-angled triangle, or a right-angled triangle.
• An obtuse triangle is a triangle that has one obtuse angle and two acute angles. It becomes an obtuse scalene triangle when the two acute angles are unequal.
• A scalene triangle becomes an obtuse scalene triangle if one of its interior angles is an obtuse angle.

## Conclusion

In this article, we learned about the special triangle — Obtuse Scalene Triangle, along with its properties and associated formulas. Let’s move to the numerical section and solve a few examples and practice MCQs for better comprehension!

## Solved Examples on Obtuse Scalene Triangle

1. Find the perimeter of an obtuse scalene triangle whose sides are 2 inches, 6.5 inches, and 8 inches.

Solution:

Side-lengths are 2 inches, 6.5 inches, and 8 inches.

Perimeter = Sum of all sides

Perimeter = 2 in + 6.5 in + 8 in

Perimeter = 16.5 inches

2. Find the area of an obtuse scalene triangle with height 12 units and base 14 units.

Solution:

Base (b) = 14 units

Height (h) = 12 units

Area $= \frac{1}{2} \times b \times h$

Area $= \frac{1}{2} \times 14 \times 12$

Area = 84 square units

3. If the area of an obtuse scalene triangle is 24 square inches and the base is 6 inches, what will be its height?

Solution:

Area of an obtuse scalene triangle (A) = 24 square inches

Base (b) = 6 inches

Area $= \frac{1}{2} \times b \times h$

Height $= \frac{2 \times Area}{Base}$

Height $= \frac{2 \times 24}{6}$Since we know the length of all sides, we will use the Heron’s formula.

Height =8 inches

4. Find the area of the following obtuse scalene triangle.

Solution:

AB = a = 6 units

BC = b = 4 units

AC = c = 9 units

Since we know the length of all sides, we will use the Heron’s formula.

Semiperimeter $= s = \frac{a + b + c}{2} = \frac{6 + 4 + 8}{2} = \frac{18}{2} = 9$ units

Area $= \sqrt{s(s\;-\;a)(s\;-\;b)(s\;-\;c)}$

Area $= \sqrt{9(9\;-\;6)(9\;-\;4)(9\;-\;8)}$

Area $= \sqrt{8 \times 3 \times 5 \times 1}$

Area$= \sqrt{120}$

Area $= 2\sqrt{30}$ square units

5. Find the third angle of the obtuse scalene triangle whose two angles are 20° and 30°.

Solution:

In △ABC, let m∠A = 20° and m∠B = 30°.

By the angle sum property, we write

m∠A + m∠B + m∠C = 180°

20° + 30° + m∠C = 180°

50° + m∠C = 180°

m∠C = 180° – 50° = 130°

## Practice Problems on Obtuse Scalene Triangle

1

### A scalene triangle is a triangle that has

three equal sides.
three unequal sides.
three acute angles.
one right angle.
CorrectIncorrect
Correct answer is: three unequal sides.
A scalene triangle has three unequal sides.
2

### A triangle having angles 130°, 30°, and 20° is

an acute scalene triangle.
a right scalene triangle.
an isosceles triangle.
an obtuse scalene triangle.
CorrectIncorrect
Correct answer is: an obtuse scalene triangle.
In an obtuse scalene triangle, there is one obtuse angle and two acute angles. Note that since three angles are of different measure, the sides must be of different lengths. So, it is an obtuse scalene triangle.
3

### The three angles of a triangle are 34°, 36° and 110°. Which type of triangle is this?

Obtuse Scalene Triangle
Obtuse Isosceles Triangle
Acute Triangle
Equilateral Triangle
CorrectIncorrect
Correct answer is: Obtuse Scalene Triangle
There is an obtuse angle and two unequal acute angles. So, the angles 34°, 36°, and 110° form an obtuse scalene triangle.
4

### Find the perimeter of the triangle given below? 4 units
6 units
8 units
10 units
CorrectIncorrect
Perimeter = Sum of all the sides
Perimeter = AB + BC + AC
Perimeter = 1.7 + 2.8 + 1.5
Perimeter = 6 units