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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.

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}. \\ $$

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