Correct Answer: 3.76 cm

Solution :
Given: A right-angled triangle ABC with AB = 8 cm and AC = 17 cm
Applying the Pythagoras theorem to the given $\triangle$ABC
⇒ We get, AC ² = AB ² + BC ²
⇒ 17 ² = 8 ² + BC ²
⇒ BC ² = 225
⇒ BC = 15 cm
Now, the above triangle ABC can be divided into two right triangles $\triangle$BDA and $\triangle$BDC.
Let the length of AD = $x$, then DC = 17 – $x$
Applying Pythagoras theorem to the two triangles we get,
⇒ BD ² = AB ² – AD ² and BD ² = BC ² – DC ²
So, AB ² – AD ² = BC ² – DC ²
⇒ 82 – $x$ ² = 15 ² – (17 – $x$) ²
⇒ 64 – $x$ ² = 225 – (289 + $x$ ² – 34$x$)
⇒ 64 – 225 + 289 = 34$x$
⇒ 128 = 34$x$
$\therefore x$ = 3.76 cm
Hence, the correct answer is 3.76 cm.