Question

The lengths of the sides of a triangle XYZ are XY = 7 cm, YZ = 11 cm and ZX = 14 cm. Find the length of the median dividing the side ZX of the triangle.
1. 4 cm
2. 6 cm
3. 8 cm
4. 10 cm

Answer 1

Correct Answer - Option 2 : 6 cm

For a triangle with sides a, b and c, the length of median dividing the side with length 'a' units is given as,

⇒ m_a = (1/2) √(2b² + 2c² – a²)

Hence, the length of the median dividing the side ZX = (1/2) √[2(XY)² + 2(YZ)² – (ZX)²]

Substituting values,

∴ Length of required median = (1/2) √[2(49) + 2(121) – (196)] = (1/2) √144 = 12/2 = 6 cm