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

(i) 3 cm, 8 cm, 6 cm

(ii) 13 cm, 12 cm, 5 cm

(iii) 1.4 cm, 4.8 cm, 5 cm

Choose the greatest length. Check whether the square of greatest length is equal to the sum of squares of other two lengths.

(i) Here greatest length is 8 cm and other lengths are 3 cm, 6 cm.

Note that 8² = 64 and 3² + 6² = 9 + 36 = 45.

Note that, 64 ≠ 45.

Hence, the triangle with given lengths of sides is not a right triangle.

(ii) Here greatest length is 13 cm and other lengths are 5 cm, 12 cm.

Note that 13² = 169 and 5² + 12² = 25 + 144 = 169.

Thus, 13² = 5² + 12².

Hence, the triangle with given lengths of sides is a right triangle and length of hypotenuse is 13 cm.

(iii) Here greatest length is 5 cm and other lengths are 1.4 cm, 4.8 cm.

Note that 5² = 25 and (4.8)² + (1.4)² = 23.04 + 1.96 = 25.

Thus, 5² = (4.8)² + (1.4)².

Hence, the triangle with given lengths of sides is a right triangle and length of hypotenuse is 5 cm.