Question : If $2r=h+\sqrt{r^{2}+h^{2}}$, then the ratio of $r:h (r\neq 0)$ is:
Option 1: $1:2$
Option 2: $2:3$
Option 3: $4:3$
Option 4: $3:5$
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Correct Answer: $4:3$
Solution : Given: $2r=h+\sqrt{r^{2}+h^{2}}$ ⇒ $2r-h=\sqrt{r^{2}+h^{2}}$ By squaring both sides, we get, ⇒ $4r^{2}+h^{2}-4rh=r^{2}+h^{2}$ ⇒ $3r^{2}=4rh$ ⇒ $3r=4h$ $\therefore r:h=4:3$ Hence, the correct answer is $4:3$.
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