Menu Close

Question-19394




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

Leave a Reply

Your email address will not be published. Required fields are marked *