Length of the sides of triangles are given. Determine which of them is a right angled triangle. In case of right angled triangle determine the hypotences.

(i) 5 cm, 4 cm, 3 cm

(ii) 10 cm, 15 cm, 13 cm

(iii) 60 cm, 80 cm, 100 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 5 cm and other lengths are 3 cm, 4 cm.

Note that 5² = 25 and 3² + 4² = 9 + 16 = 25.

Thus, 5² = 3² + 4²

Hence, the triangle with given lengths of sides is a right triangle.

(ii) Here greatest length is 15 cm and other lengths are 10 cm, 13 cm.

Note that 15² = 225 and 10² + 13² = 100 + 169 = 269.

Thus, 225 ≠ 269

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

(iii) Here greatest length is 100 cm and other lengths are 80 cm, 60 cm.

Note that 100² = 10000 and 80² + 60² = 6400 + 3600 = 10000

Thus, 10000 = 10000

Hence, the triangle with given lengths of sides is a right triangle.