Question

Verify whether the following measures are the sides of a right angled triangle.
$6$, $8$, $10$

Answer 1

Sides are : $6,8,10$
Consider the areas of square on the sides : $6^2,8^2,{10}^2$
i.e., $36,64,100$
Consider the sum of areas of squares on the two smaller sides : $36+64=100$
$6^2+8^2={10}^2$
We observe that, square on the longest side of the triangle is equal to the sum of squares on the other two sides.
By converse of Pythagoras theorem, those two smaller sides must contain a right angle.
Hence, the sides $6,8$ and $10$ form the sides of a right angled triangle with hypotenuse $10$ units, $6$ and $8$ units as the sides containing the right angle.