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