question_answer

Assertion  If the side of a rhombus is 10 cm. Its diagonals should have values 16 cm and 12 cm. Reason (R) The diagonals of a rhombus cut at right angles.

A)  A and R are correct and R is the correct explanation of A  

B)  A and R are correct but R is not correct explanation of A                         

C)  A is correct but R is wrong              

D)  A is wrong but R is correct   

Correct Answer: A

Solution :

  \[{{H}^{2}}={{P}^{2}}+{{B}^{2}}\] \[\therefore \]      \[A{{B}^{2}}+B{{C}^{2}}+C{{D}^{2}}+A{{D}^{2}}=A{{C}^{2}}+B{{D}^{2}}\] \[\Rightarrow \]\[{{(10)}^{2}}+{{(10)}^{2}}+{{(10)}^{2}}+{{(10)}^{2}}={{(16)}^{2}}+{{(12)}^{2}}\] \[\Rightarrow \]                           \[400=400\] Hence, both  and (R) are true and (R) is the correct explanation of .