Question Number 19394 by tawa tawa last updated on 10/Aug/17
Answered by allizzwell23 last updated on 10/Aug/17
$$ \\ $$$$\:\:\:\frac{\mathrm{AB}}{\mathrm{DF}}\:=\:\frac{\mathrm{AC}}{\mathrm{CE}}\:\:\mathrm{similar}\:\mathrm{triangles} \\ $$$$\:\:\mathrm{Let}\:\mathrm{AD}\:=\:\mathrm{x}\:\:\Rightarrow\:\mathrm{BF}\:=\:\mathrm{x}\:\:\:\therefore\:\mathrm{AB}\:=\:\mathrm{6}+\mathrm{2x} \\ $$$$\:\:\frac{\mathrm{2x}+\mathrm{6}}{\mathrm{6}}\:=\:\frac{\mathrm{20}}{\mathrm{12}}\:\:\:\:\Rightarrow\:\mathrm{2x}+\mathrm{6}\:=\:\frac{\mathrm{20}}{\mathrm{12}}×\mathrm{6}\:=\:\mathrm{10} \\ $$$$\:\:\:\:\:\mathrm{2x}\:=\:\mathrm{10}−\mathrm{6}\:=\:\mathrm{4} \\ $$$$\:\:\:\:\therefore\:\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\mathrm{AD}\:=\:\mathrm{2}\:\:\:\:\:\: \\ $$
Commented by tawa tawa last updated on 10/Aug/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$