A) 30 m
B) 60 m
C) 40 m
D) 50 m
Correct Answer: D
Solution :
Let the length and breadth of rectangle be x and y m, respectively. According to the question, \[2(x+y)=160\] \[\Rightarrow \] \[x+y=\frac{160}{2}=80\,\,\text{m}\] ?(i) Perimeter of square = 160 m \[\therefore \] Side of square \[=\frac{160}{4}=40\,\,\text{m}\] Now, area of rectangle = xy Area of square \[=40\times 40=1600\,\,{{\text{m}}^{\text{2}}}\] Then, \[1600-xy=100\] \[\Rightarrow \] \[xy=1600-100=1500\] ?(ii) Now, \[{{(x-y)}^{2}}={{(x+y)}^{2}}-4xy\] \[={{(80)}^{2}}-4\times 1500\] \[=6400-6000=400\] \[\Rightarrow \] \[x-y=\sqrt{400}=20\] ?(iii) From Eqs. (i) and (iii), we get \[2x=100\] \[\Rightarrow \] \[x=\frac{100}{2}=50\,\,\text{m}\]You need to login to perform this action.
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