| If the perimeter of a square is equal to the radius of a circle whose area is \[39424\,c{{m}^{2}}.\]What is the area of the square? |
A) \[1225\,\,c{{m}^{2}}\]
B) \[441\,\,c{{m}^{2}}\]
C) \[784\,\,c{{m}^{2}}\]
D) Cannot be determined
E) None of the above
Correct Answer: C
Solution :
| Perimeter of square = 4a |
| Also, \[\pi {{r}^{2}}=39424\] |
| \[\Rightarrow \] \[{{r}^{2}}=\frac{39424\times 7}{22}\] |
| \[\Rightarrow \] \[{{r}^{2}}=7\times 7\times 16\times 16\] \[\Rightarrow \] \[r=16\times 7=112\] |
| Perimeter of square =112 |
| \[\Rightarrow \] \[4a=112\]\[\Rightarrow \]\[a=28\] |
| Area of square \[={{a}^{2}}={{(28)}^{2}}=784\,\,c{{m}^{2}}\] |
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