A) \[2\sqrt{6}\,m\]
B) \[6\sqrt{0.475}\,m\]
C) \[4\sqrt{6}\,m\]
D) \[5\sqrt{6}\,m\]
Correct Answer: B
Solution :
(b): semi perimeter \[=\left( 1+b \right)\] \[\therefore \frac{h}{1+b}=\frac{6}{10}\] \[\begin{align} & h=6 \\ & 1+b=10x \\ \end{align}\] Effective area of wall \[=perimeter\times h=40\] \[=2\left( 1+b \right)h-40\] \[=2\times 10x\times 6x-40\] \[=120{{x}^{2}}-40.\] Cost to cover = area (in \[{{m}^{2}}\]) \[\times \] cost per \[{{m}^{2}}\] For 100cm (0.1 m width) and 1m length i.e. for 0.1 \[{{m}^{2}}\], cost = Rs. 10. For 1 \[{{m}^{2}}\], cost = Rs. 100. Cost to cover \[=1700=\left( 120{{x}^{2}}-40 \right)\times 100\] \[\Rightarrow 120{{x}^{2}}=57\] \[\Rightarrow x=\sqrt{\frac{57}{120}}=\sqrt{\frac{19}{40}}=\sqrt{0.475}\] \[\therefore 6x=6\sqrt{0.475}.\]
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