  Question

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 60∘then 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=AB2−OB2 ⇒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). MathematicsSecondary School Mathematics IXStandard IX

Suggest Corrections  1  Similar questions
View More  Same exercise questions
View More  People also searched for
View More 