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Explanation:

Area of ∆ACD is half of area of ∆ABD.
Since their height is same, ratio of their areas will be same as the ratio of their bases.
⇒ BD = 2CD
⇒ BD = 2 cm and CD = 1 cm.

Taking E as the midpoint of BC, BE = 3/2 = 1.5
⇒ ED = 2 – 1.5 = 0.5 cm.

Also, AE = height of the equilateral triangle = 32 × 3 = 332

In ∆AED
⇒ AD2 = AE2 + ED2
⇒ AD2 = 3322 + (0.5)2

⇒ AD2 = 274 + 14 = 7

⇒ AD = 7

Hence, option (a).

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