If the sides of a triangle are 3 cm,
Question:

If the sides of a triangle are 3 cm, 4 cm and 6 cm long, determine whether the triangle is a right-angled triangle.

Solution:

We have,

$a=3 \mathrm{~cm}$

$b=4 \mathrm{~cm}$

$c=6 \mathrm{~cm}$

In order to prove that the triangle is a right angled triangle we have to prove that square of the larger side is equal to the sum of the squares of the other two sides.

Here, the larger side is $c=6 \mathrm{~cm}$.

Hence, we have to prove that $a^{2}+b^{2}=c^{2}$.

Let solve the left hand side of the above equation.

$a^{2}+b^{2}=3^{2}+4^{2}$

$=9+16$

$=25$

Now we will solve the right hand side of the equation,

$c^{2}=6^{2}$

$=36$

Here we can observe that left hand side is not equal to the right hand side.

Therefore, the given triangle is not a right angled triangle.