A) 10 cm
B) 5 cm
C) 12 cm
D) 18 cm
Correct Answer: B
Solution :
Let the length and breadth of the rectangular field be x cm and y cm respectively. As question, \[xy=60\,\,\text{sq}\,\,\text{cm}\] ?(i) and \[\sqrt{{{x}^{2}}+{{y}^{2}}}+x=5y\] ?(ii) \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}={{(5y-x)}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}+{{y}^{2}}=25{{y}^{2}}+{{x}^{2}}+10xy\] \[\Rightarrow \]\[24{{y}^{2}}=10\times 60\]\[\Rightarrow \]\[{{y}^{2}}=5\times 5\] \[\therefore \]\[y=5\,\,\text{cm}\]and \[x=\frac{60}{5}=12\,\,\text{cm}\] \[\therefore \]Length and breadth of the rectangular field are 12 cm and 5 cm respectively.
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