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
4 units
This problem is based on the concept of the mid-point theorem in geometry. The mid-point theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and is half the length of the third side.
In triangle ABC, X and Y are midpoints of AB and AC respectively. Therefore, according to the mid-point theorem, XY is parallel to BC and XY = BC/2.
We are given that BC + XY = 12 units. Since XY = BC/2, we can substitute this into the equation:
BC + BC/2 = 12
(3/2)BC = 12
BC = (2/3) * 12 = 8 units
Now we can find XY:
XY = BC/2 = 8/2 = 4 units
Finally, we need to find BC - XY:
BC - XY = 8 - 4 = 4 units
Therefore, BC - XY is 4 units.
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