A) \[\frac{7}{4}\]
B) \[\frac{5}{4}\]
C) \[\frac{3}{4}\]
D) \[\frac{3}{2}\]
Correct Answer: A
Solution :
Sum of two sides > third side \[5+\text{ }5r>5{{r}^{2}}\Rightarrow \,\,\,{{r}^{2}}-r-1<0\] \[{{\left( r-\frac{1}{2} \right)}^{2}}\,-\,\frac{5}{4}\,<\,0\] \[\left( r-\frac{1}{2}+\frac{\sqrt{5}}{2} \right)\left( r-\frac{1}{2}-\frac{\sqrt{5}}{2} \right)<0\] \[\frac{1-\sqrt{5}}{2}\,<\,\,r<\frac{1+\sqrt{5}}{2}\,\,\approx \,\,1.618\] \[\frac{7}{4}\,>\,\frac{1+\sqrt{5}}{2}\]
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