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:
Answer & explanation
Correct answer: option 4
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.