A square lawn has a path 4 m wide around it. If the area of the path is\[196\,\,{{m}^{2}},\]then each side of the lawn is [SSC (CGL) 2014] |
A) 7.25 m
B) 9.25 m
C) 8.25 m
D) 8 m
Correct Answer: C
Solution :
Let each side of the square lawn \[=x\,\,m\] |
Then, according to the question, |
\[{{(x+4+4)}^{2}}-{{(x)}^{2}}=196\] |
\[\Rightarrow \] \[{{(x+8)}^{2}}-{{x}^{2}}=196\] |
\[\Rightarrow \]\[{{x}^{2}}+64+16x-{{x}^{2}}=196\] |
\[\Rightarrow \]\[16x=196-64=132\]\[\Rightarrow \]\[x=\frac{132}{16}=8.25\,\,m\] |
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