Question : The midpoints of AB and AC of a $\triangle$ABC are X and Y, respectively. If BC + XY = 24 units, then the value of BC − XY is:
Option 1: 5 cm
Option 2: 4 cm
Option 3: 6 cm
Option 4: 8 cm
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Correct Answer: 8 cm
Solution :
The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and half the length of the third side.
According to the question,
BC + XY = 24 ..........(1)
Since XY = $\frac{1}{2}$ of BC,
⇒ $\frac{1}{2}$BC + BC = 24
⇒ 3BC = 24 × 2
⇒ 3BC = 48
⇒ BC = 16 cm
From Eq. (1) we get,
⇒ 16 + XY = 24
⇒ XY = 8 cm
Now accordingly,
⇒ BC – XY = 16 – 8 = 8 cm
The value of BC – XY is 8 cm.
Hence, the correct answer is 8 cm.
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