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 \[=\frac{1}{2}\times 10\times 4\sqrt{6}\] \[=20\sqrt{6}\,c{{m}^{2}}\]