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.

*ADB*and*CDB*are congruent to each other because they are both 30°-60°-90° triangles and share the side*BD*.*ADB*, side*AD*is opposite to the angle 30°; therefore, the length of*AD*is half the length of hypotenuse*AB*.*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.### Related Questions to study

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