A) 30 m
B) 5 m
C) 18.75 m
D) 10 m
Correct Answer: B
Solution :
Let the width of path be x m. |
Area of rectangular field \[=38\times 32=1216\,\,{{m}^{2}}\] |
Area of rectangular field without path |
\[=(38-2x)(32-2x)\] |
\[=1216-64x-76x+4{{x}^{2}}\] |
\[=1216-140x+4{{x}^{2}}\] |
\[\therefore \]Area of the path \[=1216-1216+140x-4{{x}^{2}}\] |
\[=140x-4{{x}^{2}}\] |
\[\therefore \] \[140x-4{{x}^{2}}=600\] |
\[\Rightarrow \]\[4{{x}^{2}}-140x+600=0\] |
\[\Rightarrow \]\[{{x}^{2}}-35x+150=0\] |
\[\Rightarrow \]\[{{x}^{2}}-30x-5x+150=0\] |
\[\Rightarrow \]\[x\,\,(x-30)-5\,\,(x-30)=0\] |
\[\Rightarrow \]\[(x-5)\,\,(x-30)=0\] |
\[\Rightarrow \]\[x=5\]as\[x\ne 30\] |
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