## What is Pythagoras Theorem

According to Pythagoras theorem “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.“ It is applicable only for the right-angled triangle.Pythagoras Theorem Proof & its application is explained here.

Each side of a right triangle has a name: Where
“a” is the perpendicular or Opposite side,

“b” is the base or Adjacent,

“h” is the hypotenuse side which is the longest side.

According to the definition,

Hypotenuse2 = Perpendicular2 + Base2

h2 = a2 + b2

### Application of Pythagoras Theorem

• To find triangle is a right-angled triangle or not.
• In a right-angled triangle, we can calculate the length of any side if the other two sides are given.
• To find the diagonal of a square.

### Pythagorean Theorem Problems

Examplem1: The sides of a triangle are 4,3 & 5 units. Check if it has a right angle or not. Solution: According to Pythagoras Theorem,

Perpendicular2 + Base2 = Hypotenuse2

Perpendicular = 5 units

Base = 3 units

Hypotenuse = 4 units

42 + 32 = 52

⇒ 16 + 9 = 25

⇒ 25 = 25

L.H.S. = R.H.S.

Therefore, It is right angle.

Examplem2: The two sides of a right-angled as shown in the figure. Find the third side. Solution: Given;

Perpendicular = p units

Base = 12 units

Hypotenuse = 15 units

As per the Pythagorean Theorem, we have;

Perpendicular2 + Base2 = Hypotenuse2

⇒p2 + 122 = 152

⇒p2 + 144 = 225

⇒p2 = 225 – 144

⇒p2 = 81

⇒p = √81
Therefore, p = 9 units