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  1. 4
  2. 6
  3. 6 square root of 2
  4. 6 square root of 3

hintHint:

Hint:- Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
In 30°-60°-90° Triangles, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

The correct answer is: 6


    Solution:-
    We have given that,
    Angle ABD = 30°
    So, by angle sum property of triangle In triangle ABD,
    Angle BAD = 60°
    Angle BCD = 60°
    by angle sum property of triangle In triangle BCD,
    Angle DBC = 30°
    • Triangles ADB and CDB are congruent to each other because they are both 30°-60°-90° triangles and share the side BD .
    • In triangle ADB, side AD is opposite to the angle 30°; therefore, the length of AD is half the length of hypotenuse AB .
    l(AD) = (½)AB
    •  Since the triangles are congruent,
    AB = BC = 12.
    • As , l(AD) = (½)AB
    l(AD)= (½)12
    l(AD)= 6
    • Therefore, the correct option is B) 6
    Note:- Option A is incorrect. If the length of AD were 4, then the length of AB would be 8. However, this is incorrect because AB is congruent to BC , which has a length of 12.
    • Options C and D are also incorrect. Following the same procedures as used to test choice A gives AB a length of for choice C and  for choice D. However, these results cannot be true because AB is ongruent to BC , which has a length of 12.

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