Question

Verify whether the following measures are the sides of a right angled triangle.
$4$, $5$, $6$

Answer 1

Sides are : $4,5,6$
Areas of squares on the sides : $4^2,5^2,6^2$
i.e., : $16,25,36$
Sum of areas of squares on the two smaller sides : $16+25=41$
$\Rightarrow$ $4^2+5^2\ne 6^2$
We observe that the square on the longest side of the triangle is not equal to the sum of the squares on the other two sides.
By converse of Pythagoras theorem, these two sides cannot contain a right angle.
Hence, $4,5$ and $6$ cannot form the sides of right angled triangle.