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

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.