discuss the method of deciding whether a triangle is right anglewe know the lengths of sides only
The sides a, b and c of a right angled triangle by the Pythagorean Theorem follow the relation a^2 = b^2 + c^2 where a is the hypotenuse.
To determine if a triangle is right angled given only the length of the sides check if they can be related such that the longest side is equal to the sum of the squares of the others.
If you can it is a right triangle. If it is not possible to do that, it is not a right angled triangle.
an example with the following lengths:10; 49,5 ; 50,5 cm
If the given lengths of the sides would be of the right angle triangle, the square of the biggest side has to result from the sum of the squares of the others.
We'll identify the biggest length, that is 50.5.
We'll apply Pythagorean theorem and we'll get:
50.5^2 = 10^2 + 49.5^2
We'll compute the squares and we'll get:
2550.25 = 100 + 2450.25
We'll compute the sum:
2550.25 = 2550.25
Since the results from both sides are the same, that means that 50.5cm represents the length of the hypotenuse and the other lengths, 10cm and 49.5cm, are of the legs of the right angle triangle.