Triangles ADB and CDB are congruent to each other because they are both
30°−60°−90° triangles and share the side
. In triangle ADB, side
is opposite to the angle
30°; therefore, the length of
is half the length of hypotenuse
. Since the triangles are congruent,
AB=BC=12. So the length of
is
=6 Choice A is incorrect. If the length of
were 4, then the length of
would be 8. However, this is incorrect because
is congruent to
,which has a length of
12. Choices C and D are also incorrect. Following the same procedures as used to test choice A gives
a length of
12√2 for choice C and
12√3 for choice D. However, these results cannot be true because
is congruent to
,which has a length of
12.