Maths-
General
Easy
Question
- 4
- 6
Hint:
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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