Right Scalene Triangle
A right scalene triangle is a triangle in which all three sides are different in length and one angle is equal to 90 degrees. A triangle is a closed figure made up of three lines and three angles. There are different types of triangles based on the side lengths and angles like a right triangle, scalene triangle, equilateral triangle, etc. A right scalene triangle is one such type of triangle that contains the properties of a right triangle and a scalene triangle.
1.  What is a Right Scalene Triangle? 
2.  Properties of a Right Scalene Triangle 
3.  Right Scalene Triangle Formulas 
4.  FAQs on Right Scalene Triangle 
What is a Right Scalene Triangle?
In geometry, a right scalene triangle can be considered as the triangle that contains the properties of both a right triangle and a scalene triangle. Let us recollect the meaning of right triangles and scalene triangles.
 A right triangle is one in which one interior angle measures 90° and the other two angles are acute angles (less than 90°). There are three sides whose lengths share the following relationship: Hypotenuse^{2} = Perpendicular^{2} + Base^{2}.
 A scalene triangle is one in which all three sides and angles are different in measurements. There is no specific relationship between the side lengths.
Observe the figure given below to understand how a scalene right triangle appears.
Properties of a Right Scalene Triangle
It is easy to identify a right scalene triangle if we know its properties. The properties of the right scalene triangle are listed below:
 All three sides are different in measurements.
 All three angles are different in measurement with one angle of 90°
 The sides of a right scalene triangle share the following relationship: Hypotenuse^{2} = Perpendicular^{2} + Base^{2}. This relationship is known as the Pythagoras theorem.
 The side opposite to the right angle is the longest side known as hypotenuse.
 The sum of all the interior angles is 180°
 A 306090 triangle is a perfect example of a right scalene triangle.
Right Scalene Triangle Formulas
The formula of a right scalene triangle is useful to find the area and perimeter of the triangle. There are two possible formulas that can be used to find the area of a right scalene triangle based on what information is given to us.
 If the length of base and height of the triangle is given, then area = [1/2 × base × height]
 If the length of all three sides are given, then area = √s(sa)(sb)(sc), where 's' is the semi perimeter = perimeter/2 = (a + b + c)/2.
To find the right scalene triangle perimeter, we just need to add the length of all three sides. So, the perimeter of a right scalene triangle = (a + b + c), where a, b, and c are the sides of the triangle.
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Right Scalene Triangle Examples

Example 1: Find the area of a right scalene triangle if the base is 10 units and the height is 8 units.
Solution: Given, base (b) = 10 units and height (h) = 8 units. The formula to calculate the area is 1/2 × b × h. By substituting the values, we get area = 1/2 × 10 × 8.
⇒ Area = 5 × 8 = 40
Therefore, the area of the given right scalene triangle is 40 square units.

Example 2: What will be the perimeter of a right scalene triangle if the sides are of lengths 5 units, 12 units, and 13 units?
Solution: The perimeter is the sum of all the sides of a shape. Here, the given three side lengths are 5 units, 12 units, and 13 units. So, the perimeter = 5 + 12 + 13 units, which is 30 units. Therefore, the perimeter of the given scalene right triangle is 30 units.

Example 3: Find the length of the hypotenuse of a right scalene triangle if base = 5 inches and perpendicular = 4 inches.
Solution: The relation between the sides of a right scalene triangle is Hypotenuse^{2} = Perpendicular^{2} + Base^{2}. By substituting the values given in the question, we get h^{2} = 5^{2} + 4^{2}.
⇒ h^{2} = 25 + 16
⇒ h^{2} = 41
⇒ h = √41 inches
Therefore, the length of the hypotenuse is √41 inches.
FAQs on Right Scalene Triangle
What is a Right Scalene Triangle?
A right scalene triangle is a triangle that contains the properties of both the right triangle and scalene triangle. It comes in the category of both right triangles and scalene triangles. One of its angles measures 90°and all the sides and angles are different in measurements.
What is the Area of a Right Scalene Triangle?
The area of a scalene right triangle can be calculated by using the formula: Area = 1/2 × base × height. The perpendicular of the right scalene triangle can be taken as the height and the side adjacent to it other than hypotenuse is the base.
How to Draw a Right Scalene Triangle?
To draw a right scalene triangle, the first step is to draw two perpendicular line segments of different measurements. Then, we can simply join the opposite ends of both to form a right scalene triangle.
How to Find the Hypotenuse of a Right Scalene Triangle?
The hypotenuse is the longest side of a right triangle which is opposite to the 90degree angle. To find the length of the hypotenuse, we need to use the following formula which expresses the relation between three sides of a right scalene triangle: Hypotenuse^{2} = Perpendicular^{2} + Base^{2}. This formula is known as the Pythagoras theorem.
What does a Right Scalene Triangle Look Like?
A right scalene triangle looks like a right triangle with two perpendicular sides forming an angle of 90 degrees. All the three angles of a right scalene triangle are different in measurement.
How to Find the Angles of a Right Scalene Triangle?
In a right scalene triangle, the sum of both the acute angles is 90° and the third angle is equal to 90°. So, if any one of the acute angles is given, then we can easily find the third angle by subtracting the given acute angle from 90.
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