Question

In ∆ABC, AB = 10, AC = 7, BC = 9, then find the length of the median drawn from point C to side AB.

Answer 1

Let CD be the median drawn from the vertex C to side AB.

`"BD" = 1/2 × "AB"`              ...(D is the midpoint of AB)

∴ BD = `1/2 × 10`

∴ BD = 5 units

In ∆ABC,

seg CD is the median.                 ...(Given)

By Apollonius theorem,

∴ AC² + BC² = 2CD² + 2BD²

∴ 7² + 9² = 2CD² + 2(5)²

∴ 49 + 81 = 2CD² + 2 × 25

∴ 130 = 2CD² + 50

∴ 2CD² = 130 − 50

∴ CD² = `80/2`

∴ CD² = 40

Taking square root of both sides,

∴ CD = `sqrt(40)`

∴ CD = `sqrt(4 × 10)`

∴ CD = `2sqrt(10)`

Hence, the length of the median drawn from point C to side AB is `2sqrt(10)` units.