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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

$$$$$$\frac{\mathrm{AB}}{\mathrm{DF}}=\frac{\mathrm{AC}}{\mathrm{CE}}\mathrm{similar}\mathrm{triangles}$$$$\mathrm{Let}\mathrm{AD}=\mathrm{x}\Rightarrow \mathrm{BF}=\mathrm{x}\therefore \mathrm{AB}=6+2\mathrm{x}$$$$\frac{2\mathrm{x}+6}{6}=\frac{20}{12}\Rightarrow 2\mathrm{x}+6=\frac{20}{12}\times 6=10$$$$2\mathrm{x}=10-6=4$$$$\therefore \mathrm{x}=2$$$$\mathrm{AD}=2$$

Commented by tawa tawa last updated on 10/Aug/17

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

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