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Question-209965




Question Number 209965 by mnjuly1970 last updated on 27/Jul/24
Answered by mr W last updated on 27/Jul/24
Commented by mr W last updated on 27/Jul/24
((AD)/(DB))=((AD)/(FH))=(1/2) ⇒((AD)/(AB))=(1/3)  ((AE)/(AC))=((AD)/(FG))=(1/2)  ((ΔADE)/(ΔABC))=((AE×AD)/(AC×AB))=(1/2)×(1/3)=(1/6)
$$\frac{{AD}}{{DB}}=\frac{{AD}}{{FH}}=\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\frac{{AD}}{{AB}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\frac{{AE}}{{AC}}=\frac{{AD}}{{FG}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\frac{\Delta{ADE}}{\Delta{ABC}}=\frac{{AE}×{AD}}{{AC}×{AB}}=\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$
Commented by mnjuly1970 last updated on 27/Jul/24
thx alot sir
$${thx}\:{alot}\:{sir} \\ $$

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