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