In triangle ABC, let X and Y be the midpoints of sides AB and AC respectively. If \(BC + XY = 12\) units, then what is the value of \(BC - XY\)?

Q.In triangle ABC, let X and Y be the midpoints of sides AB and AC respectively. If \(BC + XY = 12\) units, then what is the value of \(BC - XY\)?

Since X and Y are the midpoints of AB and AC respectively in triangle ABC, Therefore, \(XY = \cfrac{1}{2}BC\) So, \(BC + \cfrac{1}{2}BC = 12\) ⇒ \(\cfrac{3}{2}BC = 12\) ⇒ \(BC = 12 \times \cfrac{2}{3} = 8\) units Therefore, \(XY = 12 - 8 = 4\) units ⇒ \(BC - XY = 8 - 4 = 4\) units