Question Number 203017 by mnjuly1970 last updated on 07/Jan/24
Answered by som(math1967) last updated on 07/Jan/24
$${let}\:{ar}\:{ofEDCF}={a}\:,\bigtriangleup{AEB}={b} \\ $$$$\frac{\bigtriangleup{ABD}}{\bigtriangleup{BCD}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\frac{{Green}+{b}}{{Magenta}+{a}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\frac{\bigtriangleup{ABF}}{\bigtriangleup{ACF}}=\frac{{x}}{\mathrm{6}} \\ $$$$\Rightarrow\frac{{Majenta}+{b}}{{Green}+{a}}=\frac{{x}}{\mathrm{6}} \\ $$$$\Rightarrow\frac{{Green}+{b}}{{Majenta}+{a}}=\frac{{x}}{\mathrm{6}} \\ $$$$\Rightarrow\frac{\mathrm{3}}{\mathrm{4}}=\frac{{x}}{\mathrm{6}}\Rightarrow{x}=\mathrm{4}.\mathrm{5}\:{unit} \\ $$
Answered by mr W last updated on 07/Jan/24
Commented by mr W last updated on 07/Jan/24
$$\Delta{AFB}=\Delta{AEB}+{magenta} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\Delta{AEB}+{green} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\Delta{ADB} \\ $$$$\Rightarrow{DF}//{AB} \\ $$$$\Rightarrow\frac{\mathrm{4}}{\mathrm{3}}=\frac{\mathrm{6}}{{x}} \\ $$$$\Rightarrow{x}=\frac{\mathrm{3}×\mathrm{6}}{\mathrm{4}}=\mathrm{4}.\mathrm{5} \\ $$