Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse.

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 8 cm, 6 cm

(iii) 50 cm, 80 cm, 100 cm

(iv) 13 cm, 12 cm, 5 cm

(i) Geven: sides of the triangle are 7 cm, 24 cm, and 25 cm

Squaring the lengths of these sides, we get: 49, 576, and 625.

49 + 576 = 625

Or, 7² + 24² = 25²

The sides of the given triangle satisfy Pythagoras theorem

Hence, it is a right triangle

We know that the longest side of a right triangle is the hypotenuse

Therefore, the length of the hypotenuse of this triangle is 25 cm

(ii) It is given that the sides of the triangle are 3 cm, 8 cm, and 6 cm

Squaring the lengths of these sides, we will obtain 9, 64, and 36

However, 9 + 36 ≠ 64

Or, 32 + 62 ≠ 82

Clearly, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side

Therefore, the given triangle is not satisfying Pythagoras theorem

Hence, it is not a right triangle

(iii)Given that sides are 50 cm, 80 cm, and 100 cm.

Squaring the lengths of these sides, we will obtain 2500, 6400, and 10000.

And, 2500 + 6400 ≠ 10000

Or, 502 + 802 ≠ 1002

Now, the sum of the squares of the lengths of two sides is not equal to the square of the length of the third side

Therefore, the given triangle is not satisfying Pythagoras theorem

Hence, it is not a right triangle

(iv)Given: Sides are 13 cm, 12 cm, and 5 cm

Squaring the lengths of these sides, we get 169, 144, and 25.

Clearly, 144 +25 = 169

Or, 12² + 5² = 13²

The sides of the given triangle are satisfying Pythagoras theorem

Therefore, it is a right triangle

We know that the longest side of a right triangle is the hypotenuse

Therefore, the length of the hypotenuse of this triangle is 13 cm