question_answer

If the sum of the diagonal of a rhombus is 10 cm and its perimeter is \[4\sqrt{13}\,cm\], then the lengths of its diagonals are

A)  5, 5                                       

B)  6, 4  

C)  7,3                        

D)  8,2

Correct Answer: B

Solution :

 (i) All the four sides of a rhombus are equal (ii) Diagonals of a rhombus are mutually perpendicular and bisect each other \[\therefore \]  \[4a=4\sqrt{13}\] \[\Rightarrow \]               \[a=\sqrt{13}\] and \[2x+2y=10\] \[\Rightarrow \]               \[x+y=5\]                            ??(i) Also from \[\Delta \,OCD,\,{{x}^{2}}+{{y}^{2}}=13\]   .....(ii)                 Solving equations (i) and (ii), we get \[x=3\] and \[y=2\] \[\therefore \]   Diagonals are 6 and 4.