Triangle is a three-sided polygon. In simple words, a triangle is a closed two-dimensional figure with three sides and three angles. Equilateral triangle, isosceles triangle, and scalene triangle are three different types of triangles based on their sides. A scalene triangle is a triangle with all of its sides of different lengths. It means that all three angles of a scalene triangle are of different measures and all three sides are of different lengths. For example, a triangle with side lengths of 3cm, 4 cm, and 5 cm would be a scalene triangle.

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## What Do You Mean by Scalene Triangle?

A scalene triangle is one in which all three sides are of different lengths and all three angles have different measurements and less than 90 degrees. But the sum of all the angles of the scalene triangle is always 180 degrees. For example, the triangle PQR is scalene because each of the three sides, PQ = 7 cm, QR = 9 cm, and PR= 4 cm, is of uneven length. There are many places in the construction industry where triangles are used because of their stability. Scalene triangles can be seen, for example, in roof trusses.

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## Perimeter of a Scalene Triangle

A scalene triangle’s perimeter is equal to the sum of its sides. If the length of a scalene triangle’s sides is x, y, and z units, then the perimeter is calculated as follows:

**Perimeter of Scalene Triangle equals (x + y + z) units.**

## Area of a Scalene Triangle

The area of a scalene triangle is the amount of space it occupies on a two-dimensional surface. So, if you know the length of its base and the height, or the length of its three sides, you may compute the area of a scalene triangle. As a result,** the scalene triangle’s area = ½ * base * height**

Or,

The area of a scalene triangle using Heron’s formula = s(s-p)(s-q)(s-r) sq. units

Where, ‘p’, ‘q’ and ‘’r are the length of sides of the scalene triangle And, s = semi-perimeter of triangle = p+q+r/ 2

## Properties of a Scalene Triangle

Important properties of the scalene triangle

- The triangle’s sides are unequal, and the angles are of varied sizes.
- It doesn’t have a symmetry line or a symmetry point.
- A scalene triangle’s angles might be acute, obtuse, or right.
- The biggest angle in a scalene triangle is the angle opposite the longest side, and the smallest angle is the angle opposite the shortest side.
- The Sum of all the angles of the scalene triangle is 180 degrees

## Acute Triangle

An acute-angled triangle is one in which each of the triangle’s three internal angles is less than 90 degrees. For example, a triangle with interior angles 40°, 65°, and 75° is an acute angled triangle because each of the interior angles is less than 90°.

## Acute Triangle Properties

The following are some of the most important qualities of an acute triangle:

- With varied side measures, the interior angles of a triangle are always less than 90°.
- The line traced from the triangle’s base to the opposite corner is always perpendicular in an acute triangle.

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## Examples

**Example1: **Find the area of the scalene triangle XYZ with the sides 7 cm, 8 cm and 9 cm.

**Solution:**

Let p= 7 cm

q = 8 cm

r = 9 cm

If all the sides of a triangle are known, the area can be calculated using Heron’s formula.

Area of triangle = s(s-p)(s-q)(s-r)

Now, substitute the value of p,q,r in the formula of the semi perimeter

s = (p+q+r)/2

s = (7+8+9)/2

s = 24/2

s = 12

Now substitute the value of “s” in the area formula,

Area = 12(12-7)(12-8)(12-9)

=12(5)(4)(3)

=√720

=26.83

Therefore, the area of the scalene triangle = 26.83 cm2

**Example 2**:** **If the sides of a Scalene triangle are 10 cm, 7 cm and 9 cm. Find its perimeter.

**Solution:** Given, the lengths of sides of the triangle are 10cm, 7cm and 9 cm.

Perimeter of a Scalene Triangle = 10 + 7 + 9 = 26 cms

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