Correct Option: C

Firstly , We draw a figure of triangle ABC

Given , BD = 3 cm
CD = 4 cm
In ∆ ABC,
AB² + AC² = 7²
⇒ AB² + AC² = 49 ....(i)
In ∆ ABD,
AB² = AD² + 3²
AB² = AD² + 9 ....(ii)
In ∆ ADC,
AC² = AD² + 16 ....(iii)
On adding equations (ii) and (iii),
AB² + AC² = AD² + 9 + AD² + 16
⇒ 49 = 2AD² + 25
⇒ 2AD² = 49 – 25 = 24
⇒ AD² = 12
⇒ AD = √12 = 2√3 cm.