Question Number 160353 by Tawa11 last updated on 28/Nov/21
Answered by mr W last updated on 28/Nov/21
Commented by mr W last updated on 28/Nov/21
$${AC}=\mathrm{3} \\ $$$${AD}=\sqrt{\mathrm{1}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} −\mathrm{2}×\mathrm{1}×\mathrm{3}×\frac{\mathrm{1}}{\mathrm{2}}}=\sqrt{\mathrm{7}} \\ $$$$\frac{{ED}}{{DC}}=\frac{{DC}}{{AD}}\:\Rightarrow{ED}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}}} \\ $$$$\frac{{EC}}{{DC}}=\frac{{AC}}{{AD}}\:\Rightarrow{EC}=\frac{\mathrm{3}}{\:\sqrt{\mathrm{7}}}={AF} \\ $$$${EF}={a}=\sqrt{\mathrm{7}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}}}−\frac{\mathrm{3}}{\:\sqrt{\mathrm{7}}}=\frac{\mathrm{3}}{\:\sqrt{\mathrm{7}}} \\ $$$$\frac{{area}\:{small}\:{triangle}}{{area}\:{big}\:{triangle}}=\left(\frac{{a}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{7}} \\ $$
Commented by Tawa11 last updated on 28/Nov/21
$$\mathrm{Wow},\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate}. \\ $$