Triangle is a much common shape as a polygon and it has the minimum number of sides. It has three sides and three vertices. The popular types of triangles are equilateral, isosceles, scalene and right-angled triangle. In this section, the student will learn about the properties of the right-angled triangle and related terms. It is also known as a right triangle. This article will explain the right triangle formula in an easy way with examples. Let us learn it!

## What is a Right Triangle?

A right triangle is the one in which the measure of exactly one of the interior angles is 90 degrees. It is obvious that if the other two angles are equal, then each will be of 45 degrees. Such a triangle is known as an isosceles right-angled triangle. But, if the other two angles are unequal, then it is a scalene right-angled triangle.

Source: en.wikipedia.org

In it, the side opposite to the right angle will be the longest side i.e. hypotenuse of the triangle. We may give the name the other two sides as the base or perpendicular.

In mathematics, one common application of right-angled triangles is in the trigonometry branch. Actually, the relation between the angles and sides is the base for trigonometry. Let us now look at the Right Triangle Formula.

### Right Triangle Formulas

- Area of a right triangle: \(A = \frac{1}{2} B \times P\). Where B and P are the base and height of the triangle respectively.
- The perimeter of a right triangle:s = a + b + c. Where sides are a,b,c.
- Pythagoras Theorem Formula: Pythagoras has defined the relationship between the three sides of a right-angled triangle. It is a very important and useful theorem. Thus, if the measure of any two sides of a right triangle is given, then we can use the Pythagoras Theorem to find out the third side. Its statement is: \(H^ {2} = P^ {2} + B^ {2}\). Where, H is the hypotenuse, P is the perpendicular and B is the base.

## Solved Examples for Right Triangle Formula

Q.1: The length of two sides of a right-angled triangle is given as 6 cm and 8 cm. Compute the following:

- Length of its hypotenuse
- The perimeter of the triangle
- Area of the triangle

Solution: Given parameters are:

One side B = 6 cm

Other side P = 8 cm

(i) The length of the hypotenuse will be as follows:

\(H^{2} = P^{2} + B^{2}\)

Substituting the values,

\(H^{2} = 8^{2} + 6^{2}\\ = \sqrt{100} = 10 cm.\)

(ii) The perimeter of the right triangle is,

s = a + b + c = 6 + 8 + 10 = 24 cm

(iii) Area of a right triangle will be:

\(A = \frac{1}{2} \times b \times h\\\)

\(A = \frac{1}{2} \times 6 \times 8\\ = 24 cm^{2}\)

Q.2: The perimeter of a right-angled triangle is 32 cm and height and hypotenuse as 10 cm and 13 cm respectively. Find out the area of the triangle.

Solution: Given parameters are:

Perimeter, s = 32 cm

Hypotenuse, H = 13 cm

Height, P = 10 cm

Third side, B =?

We know that perimeter is computed as:

s = H + P + B

So, B = 32 – (13 + 10)

B = 9 cm

Now, \(Area = \frac{1}{2}\times b \times h\)

\(A = \frac{1}{2}\times 9 \times 10 = 45 cm^{2}\)

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