A) \[540\,\text{c}{{\text{m}}^{\text{2}}}\]
B) \[1080\,\text{c}{{\text{m}}^{\text{2}}}\]
C) \[2160\,\text{c}{{\text{m}}^{2}}\]
D) \[4320\,\text{c}{{\text{m}}^{2}}\]
Correct Answer: D
Solution :
Radius of circular wire \[=\frac{42}{2}=21\,cm\] Circumference of wire \[=2\pi r\] \[=2\times \frac{22}{7}\times 21=132\,cm\] Let the length and breadth of rectangle be 6x and 5x en respectively. \[\therefore \] Perimeter of rectangle \[=2(6x\text{+}5x)=22x\] According to the question, \[22x=132\] \[\Rightarrow \] \[x=\frac{132}{22}=6\] \[\therefore \] Length of rectangle \[=6x=6\times 6=36\,cm\] Breadth of rectangle \[=5x=5\times 6=30\,cm\] \[\therefore \] Area \[=36\times 30=1080\,c{{m}^{2}}\]
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