A) \[144\,\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[225\,\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[336\,\,\text{c}{{\text{m}}^{\text{2}}}\]
D) \[400\,\,\text{c}{{\text{m}}^{\text{2}}}\]
Correct Answer: C
Solution :
Perimeter of rhombus \[=2\sqrt{d_{1}^{2}+d_{2}^{2}}\] Where \[{{d}_{1}}\] and \[{{d}_{2}}\] are diagonals \[=2\sqrt{d_{1}^{2}+d_{2}^{2}}=100\] \[\Rightarrow \] \[=\sqrt{d_{1}^{2}+d_{2}^{2}}=50\] \[\Rightarrow \] \[=d_{1}^{2}+d_{2}^{2}=2500\] \[\Rightarrow \] \[={{(14)}^{2}}+d_{2}^{2}=2500\] \[\Rightarrow \] \[=d_{2}^{2}=2500-196=2304\] \[\therefore \] \[{{d}_{2}}=\sqrt{2304}=48\] \[\therefore \] Area of the rhombus \[=\frac{1}{2}{{d}_{1}}\times {{d}_{2}}\] \[=\frac{1}{2}\times 14\times 48=336\,\,\text{sq}\,\,\text{cm}\]
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