Question : The midpoints of AB and AC of a $\triangle ABC$ are X and Y, respectively. If BC + XY = 18 cm, then the value of BC – XY is:
Option 1: 12 cm
Option 2: 6 cm
Option 3: 8 cm
Option 4: 4 cm
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Correct Answer: 6 cm
Solution :
In $\triangle ABC$, $XY\parallel BC$ and $XY = \frac{1}{2}BC$. Given: $BC + XY = 18$ cm So, $BC + \frac{1}{2}BC = 18$ ⇒ $BC = \frac{18}{1.5} = 12$ The length of $BC$ is 12 cm. $BC - XY = BC - \frac{1}{2}BC = \frac{1}{2}BC$ ⇒ $BC - XY = \frac{1}{2} \times 12 = 6$ Hence, the correct answer is 6 cm.
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