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This question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and  Reason (R) are true and Reason (R) correct explanation of Assertion (A).

(b) Both  Assertion (A) and  Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

Assertion (A)Reason (R)If ABCD is a rhombus whose one Median of a triangle divides itangle is 60then the ratio of the into two triangles of equal area.lenghts of its diagonals is 3:1.

The correct answer is :(a) /(b)/(c)/(d).


Solution

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
Reason (R) is clearly true.
The explanation of assertion (A)​ is as follows:
ABCD is a rhombus. So, all of its sides are equal.
Now, BC = DC
⇒∠ BDC = ∠ DBC = x°
Also, ∠ BCD = 60°
∴ x° + x° + 60° = 180°
⇒​ 2x° = 120°
⇒​ x° = 60°
∴ ∠ BCD = ∠ BDC = ∠ DBC = 60°
So, ​∆ BCD is an equilateral triangle.
i.e., BD = BC = a
∴ OB = a2
Now, in ∆ OAB, we have:
OA2=AB2OB2

OA=3a2

AC=2×3a2=3a
AC:BD=3a:a=3:1
Thus, assertion (A)​ is also true, but reason (R) does not give (A).
Hence, the correct answer is (b).


Mathematics
Secondary School Mathematics IX
Standard IX

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