How to check if triangle is right angled?

Let’s take an example

 

Can 3, 4, 5 be the side of a right angled triangle?

 

We know that,

  Hypotenuse is the longest side.

 

So, Hypotenuse = 5

 

Checking Pythagoras Theorem

(Hypotenuse) ² = (Base) ² + (Height) ²

Since LHS = RHS,

Pythagoras Theorem is satisfied

 

Hence,

  3, 4, 5 form sides of a right triangle,

  with Hypotenuse = 5

 

Can 8, 15, 17 be the sides of a right angled triangle?

We know that,

  Hypotenuse is the longest side.

 

So, Hypotenuse = 17

 

Checking Pythagoras Theorem

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

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

Pythagoras theorem is satisfied

 

Hence,

8, 15, 17 form sides of a right triangle with

  Hypotenuse = 17

  Base = 8

  Perpendicular = 15

 

Can 7, 8, 10 be the sides of a right angled triangle?

We know that,

  Hypotenuse is the longest side.

 

So, Hypotenuse = 10

 

Checking Pythagoras Theorem

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

Since L.H.S ≠ R.H.S

 

Hence,

7, 8, 10 do not form sides of a right triangle

 

Can 9, 40, 41 be the sides of a right angled triangle?

We know that,

  Hypotenuse is the longest side.

 

So, Hypotenuse = 41

 

Checking Pythagoras Theorem

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

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

Pythagoras theorem is satisfied

 

Hence,

9, 40, 41 form sides of a right triangle with

  Hypotenuse = 41

  Base = 9

  Perpendicular = 40