Question Number 175294 by zzzrot last updated on 26/Aug/22
Answered by Rasheed.Sindhi last updated on 26/Aug/22
$${In}\:{triangle}: \\ $$$${a}:{the}\:{opposite}\:{side}\:{to}\:{the}\:{angle}\:{of} \\ $$$${measure}\:\mathrm{30}. \\ $$$${c}\::\:{hypotenuse}=\mathrm{2}{a} \\ $$$${a}^{\mathrm{2}} +\mathrm{6}^{\mathrm{2}} =\left(\mathrm{2}{a}\right)^{\mathrm{2}} \\ $$$$\mathrm{3}{a}^{\mathrm{2}} =\mathrm{36}\Rightarrow{a}=\mathrm{2}\sqrt{\mathrm{3}}\: \\ $$$${c}=\mathrm{2}{a}=\mathrm{4}\sqrt{\mathrm{3}}\: \\ $$$$ \\ $$$${The}\:{perimeter} \\ $$$$=\mathrm{6}×\mathrm{3}+\mathrm{2}\sqrt{\mathrm{3}}\:+\mathrm{4}\sqrt{\mathrm{3}}\: \\ $$$$=\mathrm{18}+\mathrm{6}\sqrt{\mathrm{3}}\: \\ $$