Question

In which of the following cases, a right triangle cannot be constructed?
(a) 12 cm, 5 cm, 13 cm
(b) 8 cm, 6 cm, 10 cm
(c) 5 cm, 9 cm, 11 cm
(d) None of these

Answer 1

In (a)
12² + 5² = 13²
⇒ 144 + 25 = 169
⇒ 169 = 169
Since, the sum of the square of two smallest side is equal to the square of largest side.
Hence, a right triangle can be constructed.

In (b)
8² + 6² = 10²
⇒ 44 + 36 = 100
⇒ 100 = 100
Since, the sum of the square of two smallest side is equal to the square of largest side.
Hence, a right triangle can be constructed.

In (c)
5² + 9² ≠ 11²
⇒ 25 + 81 ≠ 121
⇒ 106 ≠ 121
Since, the sum of the square of two smallest side is not equal to the square of largest side.
Hence, a right triangle can not be constructed.
Hence, the correct answer is option (c).