Solve this following


If $5,5 \mathrm{r}, 5 \mathrm{r}^{2}$ are the lengths of the sides of a triangle, then $\mathrm{r}$ cannot be equal to:


  1. $\frac{3}{2}$

  2. $\frac{3}{4}$

  3. $\frac{5}{4}$

  4. $\frac{7}{4}$

Correct Option: , 4


$\mathrm{r}=1$ is obviously true.

Let $0<\mathrm{r}<1$

$\Rightarrow \quad r+r^{2}>1$

$\Rightarrow r^{2}+r-1>0$


$\Rightarrow r-\frac{-1-\sqrt{5}}{2}$ or $r>\frac{-1+\sqrt{5}}{2}$

$r \in\left(\frac{\sqrt{5}-1}{2}, 1\right)$


When $r>1$

$\Rightarrow \frac{\sqrt{5}+1}{2}>\frac{1}{\mathrm{r}}>1$

$\Rightarrow \mathrm{r} \in\left(\frac{\sqrt{5}-1}{2}, \frac{\sqrt{5}+1}{2}\right)$

Now check options

Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now