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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=3 AD=(√(1^2 +3^2 −2×1×3×(1/2)))=(√7) ((ED)/(DC))=((DC)/(AD)) ⇒ED=(1/( (√7))) ((EC)/(DC))=((AC)/(AD)) ⇒EC=(3/( (√7)))=AF EF=a=(√7)−(1/( (√7)))−(3/( (√7)))=(3/( (√7))) ((area small triangle)/(area big triangle))=((a/3))^2 =(1/7)

$${AC}=\mathrm{3} \\ $$$${AD}=\sqrt{\mathrm{1}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} −\mathrm{2}×\mathrm{1}×\mathrm{3}×\frac{\mathrm{1}}{\mathrm{2}}}=\sqrt{\mathrm{7}} \\ $$$$\frac{{ED}}{{DC}}=\frac{{DC}}{{AD}}\:\Rightarrow{ED}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}}} \\ $$$$\frac{{EC}}{{DC}}=\frac{{AC}}{{AD}}\:\Rightarrow{EC}=\frac{\mathrm{3}}{\:\sqrt{\mathrm{7}}}={AF} \\ $$$${EF}={a}=\sqrt{\mathrm{7}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{7}}}−\frac{\mathrm{3}}{\:\sqrt{\mathrm{7}}}=\frac{\mathrm{3}}{\:\sqrt{\mathrm{7}}} \\ $$$$\frac{{area}\:{small}\:{triangle}}{{area}\:{big}\:{triangle}}=\left(\frac{{a}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{7}} \\ $$

Commented by Tawa11 last updated on 28/Nov/21

Wow, God bless you sir. I appreciate.

$$\mathrm{Wow},\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{I}\:\mathrm{appreciate}. \\ $$

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