State if the 3 lengths of the sides form a right triangle?

10 cm, 49.5 cm, 50.5 cm

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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.**

Let ABC be a triangle such that:

AB = 10

BC = 49.5

AC = 50.5

If ABC is a right angle triangle, then the longest side should be the hypotenuse such that:

hypotenuse^2 = sid(1)^2 + side(2)^2

We notice that the longest side is AC = 50.5.

Then we need to verify if (Ac)^2 = (AB)^2 + (BC)^2

==> AC^2 = AB^2 + BC^2

==> (50.4)^2 = (49.5)^2 + (10)^2

==> 2550.25 = 2450.25 + 100

==> 2550.25 = 2550.25

Then we verifies that AC^2 is a hypotenuse for the triangle ABC.

**Then, ABC is a right angle triangle.**

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