Dear student,

Given in triangle ABC , XY is a horizontal line As : XY $\parallel$ BC
$\angle$ ABC = 90$°$

AB = 12 cm
AY = 8 cm
And

We know from side splitter theorem if a line is parallel to a side of a triangle  and intersect the other two sides, then this line divides those two sides proportionally.

As we know
So , we can say that
, then we get

YC = 16 , So AC = 8 + 16 = 24 cm

Now apply Pythagoras theorem in triangle ABC

$⇒$

$⇒$  = 576 - 144

$⇒$  = 432

$⇒$BC =  $\sqrt{432}$

$⇒$BC = 20.7846  cm

So ,
AC = 24 cm And BC = 20.7846 cm           ( Ans  )
REGARDS

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