question_answer

A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn, which has an area of \[240\,{{m}^{2}}.\] If the width of the path is 3 m and the length of the plot is greater than its breadth by 2 m, what is the area of the rectangular plot?                         [LIC (AAO) 2014]

A) \[255\,{{m}^{2}}\]                  

B) \[168\,{{m}^{2}}\]

C) \[288\,{{m}^{2}}\]      

D) \[360\,{{m}^{2}}\]

E) \[224\,{{m}^{2}}\]

Correct Answer: C

Solution :

Given, width of path = 3 m

Area of plot (excluding path) \[=240\,{{m}^{2}}\]

Let breadth of plot = x

Length of plot \[=x+2\]

According to the question,

\[240=x\,(x+2)-3\times x\]

\[\Rightarrow \]\[240={{x}^{2}}-x\]

\[\Rightarrow \]   \[{{x}^{2}}-x-24=0\]

\[\Rightarrow \]\[{{x}^{2}}-16x+15x-24=0\]

\[\Rightarrow \]\[x\,(x-16)+15\,(x-16)=0\]

\[\Rightarrow \]   \[(x-16)(x+15)=0\]

\[\therefore \]      \[x=16\]

\[\therefore \] Area of plot = Length \[\times \] Breadth

\[=18\times 16=288\,{{m}^{2}}\]