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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