question_answer

A square lawn is surrounded by a path 2.5 wide. If the of the path is\[165\,\,{{m}^{2}}\]. Find the area of the lawn.

A) \[196\,\,{{m}^{2}}\]                

B) \[194\,\,{{m}^{2}}\]

C) \[169\,\,{{m}^{2}}\]                

D) \[167\,\,{{m}^{2}}\]

Correct Answer: A

Solution :

  Area of EFGH \[=(x+2.5\,\,m+2.5\,\,m)\times (x+2.5\,\,m+2.5\,\,m)\] \[={{(x+5\,\,m)}^{2}}\] Area of\[ABCD={{x}^{2}}\] \[\therefore \]Area of path \[={{(x+5\,\,m)}^{2}}-{{x}^{2}}={{x}^{2}}+25\,\,{{m}^{2}}+10x-{{x}^{2}}=165\,\,{{m}^{2}}\] \[10x=165\,\,m-25\,\,m\] \[10x=140\,\,m\] \[x=14\,\,m\] Area of lawn  \[={{x}^{2}}={{(14\,\,m)}^{2}}=196\,\,{{m}^{2}}\]