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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Answer (1)
22nd Jan, 2024
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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