Question : If $4r=h+\sqrt{r^2+h^2}$, then $r:h$ is?$(r\neq0)$
Option 1: 17 : 8
Option 2: 8 : 17
Option 3: 8 : 15
Option 4: 15 : 8
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Correct Answer: 8 : 15
Solution :
Given:
$4r=h+\sqrt{r^2+h^2}$
⇒ $4r-h=\sqrt{r^2+h^2}$
Squaring both sides we get,
⇒ $16r^2+h^2-8rh=r^2+h^2$
⇒ $15r^2=8rh$
⇒ $15r=8h$
⇒ $\frac{r}{h}=\frac{8}{15}$
Therefore, $r:h=8:15$
Hence, the correct answer is 8 :15.
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