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Pythagoras Theorem

History

Pythagoras theorem is also known by other name as Pythagorean Theorem is the famous theorem in the geometry. This theorem is based on three sides of a right angled triangle. The name of theorem was given after the name of the Greek philosopher Pythagoras. The brief history of the Pythagoras can be read from Pythagoras on Wikipedia.

There are many proofs, the mathematicians have worked on till date. Some of the proofs of Pythagoras theorem aer given at Pythagoras’s Theorem at Proof Wiki.

Theorem Statement

In a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides of the triangle.

Let’s understand it with a diagram of right angled triangle ABC, right angled at point B.

Right angle ΔABC
Right angle ΔABC

In the above right angle ΔABC, p is perpendicular, b is base and h is hypotenuse.
h2 = b2 + p2
or h = b 2 + p 2

Let’s solve the problem of finding the hypotenuse of a right angled triangle using Pythagoras theorem.

Example

Find the length of hypotenuse of right angle ΔABC, where length of base =3cm and length of perpendicular = 9cm.
Solution:
In ΔABC
b=3cm
p=4cm
∵, ΔABC is a right angle triangle          (given)
∴ by applying Pythagoras theorem
h = b 2 + p 2
h = 3 2 + 4 2
h = 9 + 16
h = 25
∴ h = 5cm

Applications of Pythagorus theorem in real life

As we have learnt above the Pythagorus theorem can calculate length of one side of a right angled triangle, if the length of the other two sides are known. The ability of theorem to find such lengths can be applied in many real life scenarios in distance calculations, where the three distances forms the shape of a right angled triangle.