​Find r .

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \mathrm{a}=30 \\ \mathrm{b}=37 \\ \mathrm{c}=13 \\ \mathrm{s}=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}=\frac{30+37+13}{2}=40 \\ \mathrm{s}-\mathrm{a}=40-30=10 \\ \mathrm{s}-\mathrm{b}=40-37=3 \\ \mathrm{s}-\mathrm{c}=40-13=27 \\ △=\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)} \\ =\sqrt{40\times 10\times 3\times 27} \\ =\sqrt{2^2\times {10}^2\times 9^2} \\ =2\times 10\times 9=180 \\ \mathrm{r}=\frac{△}{\mathrm{s}} \\ \mathrm{Put} \mathrm{the} \mathrm{values} \mathrm{and} \mathrm{find} \mathrm{the} \mathrm{answer} \\ \mathrm{r}=\frac{180}{40}=4.5 \mathrm{units} \end{gathered}$$

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