Question

what is the ratio of r1 :r2 if
$r1 \: \times \: 5\pi \div 12 = r2 \times \pi \div 3$

Answer 1

$\frac{r1}{r2} = \frac{12}{5\pi} \times \frac{\pi}{3} \\ \\ \frac{r1}{r2} = \frac{4}{5}$
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Answer 2

$\frac{r_{1} * 5\pi}{12} = \frac{r_{2} * \pi}{3} \\ \\ \frac{r_{1} * 5\pi}{12} = \frac{r_{2}}{3} * \pi \\ \\ \frac{r_{1} * 5\pi}{12} / \pi = \frac{r_{2}}{3} \\ \\ = \frac{r_{1} * 5\pi}{12} * \frac{1}{\pi} = \frac{r_{2}}{3} \\ \\ = \frac{r_{1} * 5}{12} = \frac{r_{2}}{3} \\ \\ r_{1} * 5 = \frac{r_{2}}{3} * 12 = r_{2} * 4 \\ \\ r_{1} * 5 = r_{2} * 4 \\ \\ \frac{r_{1}}{r_{2}} = \frac{4}{5} \\ \\ r_{1} : r_{2} = 4 : 5$ 

4 : 5 is the answer. 

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