question_answer

If one side and one diagonal of a rhombus are 7 cm and 10 cm respectively, then its area (in\[c{{m}^{2}}\]) is

A)  17                               

B)  12

C)  \[20\sqrt{6}\]               

D)  \[10\sqrt{6}\]

Correct Answer: C

Solution :

\[\because \] OB = 5 cm and AB = 7 cm \[\therefore \] \[OA=\sqrt{A{{B}^{2}}-O{{B}^{2}}}\]             \[=\sqrt{49-25}\]             \[=2\sqrt{6}\] \[\therefore \] \[AC=2\,\,OA=2\times 2\sqrt{6}=4\sqrt{6}\] Hence, area of rhombus \[=\frac{1}{2}\times 10\times 4\sqrt{6}\]             \[=20\sqrt{6}\,c{{m}^{2}}\]