question_answer

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,

\[{{(x+4+4)}^{2}}-{{(x)}^{2}}=196\]

\[\Rightarrow \]   \[{{(x+8)}^{2}}-{{x}^{2}}=196\]

\[\Rightarrow \]\[{{x}^{2}}+64+16x-{{x}^{2}}=196\]

\[\Rightarrow \]\[16x=196-64=132\]\[\Rightarrow \]\[x=\frac{132}{16}=8.25\,\,m\]