\( \triangle \mathrm{ABC} \) is an equilateral triangle with each side of length \( 2 x \). If \...

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\( \triangle \mathrm{ABC} \) is an equilateral triangle with each side of length \( 2 x \). If \( A D \perp B C \), then the value of \( A D \) is
a. \( \sqrt{3} \)
b. \( \sqrt{3} \mathrm{x} \)
c. \( \mathrm{x} \)
d. \( 2 \mathrm{x} \)
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