The mid points of AB and A C of a ΔABC are X and Y, respectively. If BC + XY = 24 units, then the value of BC - XY is:

8 cm

According to the question,

BC + XY = 24    ..(1)

Since XY = \(\frac{1}{2}\) of BC,

⇒ \(\frac{1}{2}\) of BC + BC = 24

⇒ 3BC = 24 x 2

⇒ 3BC = 48

⇒ BC = 16 units

From eq.(1) we get,

⇒ 16 + XY = 24

⇒ XY = 8 units

Now accordingly,

⇒ BC - XY = 16 - 8 = 8 units

Therefore, BC - XY is 8 units.