X and Y are the mid-points of sides AB and AC of a triangle

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X and Y are the mid-points of sides AB and AC of a triangle ABC. If (BC + XY) = 12 units, then (BC – XY) is

1. 8 units
2. 4 units
3. 6 units
4. 2 units

Correct Option: B

On the basis of question we draw a figure of triangle ABC in which X and Y are the mid-points of sides AB and AC ,

The line joining the mid–points of two sides of a triangle is parallel to the third side and half of the base.

∴ XY =	1	BC
	2

⇒ BC = 2XY
∴ BC + XY = 12 units
⇒ 2XY + XY = 12
⇒ 3XY = 12

⇒ XY =	12	= 4 units
	3

∴ BC = 12 – 4 = 8 units
∴ BC – XY = 8 – 4 = 4 units