A) \[\sqrt{3}:1\]
B) \[1:\sqrt{3}\]
C) \[2:\sqrt{3}\]
D) \[4:\sqrt{3}\]
Correct Answer: C
Solution :
Let the each side of equilateral triangle be a, then its perimeter = 3a Again, \[2(l+b)=3a\] \[\Rightarrow \] \[l+b=\frac{3}{2}\cdot a\] \[\Rightarrow \] \[a+b=\frac{3a}{2}\] \[\Rightarrow \] \[AB=l=a\] (for the rectangle) \[\Rightarrow \] \[b=\frac{a}{2}\] \[\therefore \] area of rectangle \[=a\times \frac{a}{2}=\frac{{{a}^{2}}}{2}\] and area of triangle \[=\frac{\sqrt{3}}{4}\times {{a}^{2}}\] \[\therefore \] Required ratio \[=\frac{{{a}^{2}}/2}{\sqrt{3{{a}^{2}}}/4}=\frac{2}{\sqrt{3}}\]
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