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Question Number 189899 by Mingma last updated on 23/Mar/23

Answered by HeferH last updated on 23/Mar/23

Commented by HeferH last updated on 24/Mar/23

$$(6-\mathrm{r})+(6\sqrt{3}-\mathrm{r})=12$$$$6+6\sqrt{3}-12=2\mathrm{r}$$$$\mathrm{r}=\frac{6\sqrt{3}-6}{2}=3\sqrt{3}-3$$$$\frac{\mathrm{x}}{3\sqrt{3}-3}=\frac{6\sqrt{3}-(3\sqrt{3}-3)}{\sqrt{{(3\sqrt{3}-3)}^2+36}}$$$$\mathrm{x}=\frac{{\left(3\sqrt{3}\right)}^2-9}{\sqrt{72-18\sqrt{3}}}=\frac{18}{\sqrt{8\cdot 9-2\cdot 9\sqrt{3}}}=\frac{18}{3\sqrt{8-2\sqrt{3}}}$$$$\mathrm{x}=\frac{6}{\sqrt{8-2\sqrt{3}}}\approx 2.81$$

Commented by Rupesh123 last updated on 24/Mar/23

Excellent!

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