Question : The midpoints of sides AB and AC of the triangle ABC are, respectively, X and Y. If (BC + XY) = 12 units, then the value of (BC – XY) is:
Option 1: 2 units
Option 2: 6 units
Option 3: 8 units
Option 4: 4 units
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Correct Answer: 4 units
Solution : Given: (BC + XY) = 12 units -- (1) Since A line joining the midpoints of two sides of a triangle is half of the third side and also parallel to it. So, XY = $\frac{1}{2}$×BC ⇒ BC = 2XY Putting the value of BC in equation (1) 2XY + XY = 12 ⇒ XY = 4 So, BC = 12 – 4 = 8 units $\therefore$ (BC – XY) = 8 – 4 = 4 units Hence, the correct answer is 4 units.
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