How to Find the Third Side of a Triangle Given Two Sides?

Triangle is a closed figure that is formed by joining three line segments. It consists of three angles and three vertices. The angles of triangles can be the same or different depending on the type of triangle. There are different types of triangles based on line and angles of the triangle. Finding the third side of the triangle is possible only in case of the right-angle triangle.

In this article, we learn about What is a Triangle? Types of Triangle, Pythagoras Theorem and Finding the third side of the Triangle and others in detail.

What is a Triangle?

A triangle is a 3-D figure which is formed by joining three line segments. It is the smallest polygon that is formed using only three sides. Various shapes around us resembles triangle that are, Paintings, Traffic Signs, Sweets, Tables, etc. others are triangle in shapes.

Learn more about,

• Area of Triangle
• Perimeter of Triangle

Properties of a Triangle

Various properties of the triangle are,

• A triangle has 3 sides. 3 angles and 3 vertices.
• Sum of all the angles of triangles is 180° this is called Angle Sum Property of Triangle.
• Perimeter of a triangle is the sum of all three sides of the triangle.
• Area of Triangle is 1/2 base times its height.

Types of Triangles

There are various types of triangles base on the measure of sides and angles of the triangle. That are, types of triangles on the basis of sides of triangle,

• Equilateral Triangle
• Isosceles Triangle
• Scalene Triangle

Types of triangles on the basis of angles of triangle.

• Acute Angled Triangle
• Right Angled Triangle
• Obtuse Angled Triangle

Finding Third Side of a Triangle given Two Sides are Given

The third side of any triangle is found only when two sides of the Right-Angled Triangle are given. We use Pythagoras Theorem in such case. Lets assume that a Right Angled Triangle ABC where, AB is the Perpendicular, BC is the Base, and CA is Hypotenuse.

Then according to Pythagoras Theorem, the sum of squares of two sides is equal to the square of the third side. 

(Perpendicular)² + (Base)² = (Hypotenuse)²

Using the above equation third side can be calculated if two sides in a right angled triangle are known. This is explained using the example added below,

Example: If two sides of a right angled triangle are, AB(Perpendicular) = 3 cm and BC (Base) = 5 cm then find the third side Hypotenuse of the triangle.

Given,

• Perpendicular (P) = 3 cm
• Base (B) = 4 cm

Using Pythagoras theorem 

P² + B² = H²

(3)² + (4)² = H²

9 + 16 = H²

25 = H²

H = 5

Thus, the third side hypotenuse of the triangle ABC CA is 5 cm.

Read, More

• Area of Isosceles Triangle
• Heron’s Formula

Problems on Pythagoras Theorem

Problem 1: Find the measure of base if perpendicular and hypotenuse is given, perpendicular = 12 cm and hypotenuse = 13 cm.

Solution:

Given,

• Perpendicular = 12 cm
• Hypotenuse = 13 cm

Using Pythagoras Theorem 

P² + B² = H²

B² = H² – P²

B² = 13² – 12²

B² = 169 – 144

B² = 25 = 5 cm

Problem 2: Perimeter of the equilateral triangle is 63 cm find the side of the triangle.

Solution:

Perimeter of an Equilateral Triangle =  3×side

3×side = 64

side = 63/3

side = 21 cm

Problem 3: Find the measure of the third side of a right-angled triangle if the two sides are 6 cm and 8 cm.

Solution:

Given,

• Perpendicular = 6 cm
• Base = 8 cm

Using Pythagoras Theorem

H² = P² + B²

H² = P² + B²

H² = 6² + 8²

H² = 36 + 64

H² = 100

H = 10 cm

Problem 4: Find the hypotenuse of a right angled triangle whose base is 8 cm and whose height is 15 cm?

Solution: 

Using Pythagorean theorem, a² + b² = c²

So 8² + 15² = c²

hence c = √(64 + 225)

c = √289 = 17 cm

FAQs

1. How to Find the Missing Side of a Triangle?

The missing side of a right angle triangle is found using the Pythagoras Theorem.

2. How to Find Area of a Triangle?

Area of a Triangle is found using the formula, Area of Triangle = 1/2(b)(h).

3. How to Find Perimeter of a Triangle?

Perimeter of Triangle is the sum of all sides in a triangle and thus, perimeter of triangle is found by adding all the sides of a triangle.

4. How to Find the Sides of a Right Triangle?

To Find the sides of a Right Triangle we use the formula, P² + B² = H². This formula is also called the Pythagoras Theorem.