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Question Number 203017 by mnjuly1970 last updated on 07/Jan/24

Answered by som(math1967) last updated on 07/Jan/24

$$letarofEDCF=a,△AEB=b$$$$\frac{△ABD}{△BCD}=\frac{3}{4}$$$$\frac{Green+b}{Magenta+a}=\frac{3}{4}$$$$\frac{△ABF}{△ACF}=\frac{x}{6}$$$$\Rightarrow \frac{Majenta+b}{Green+a}=\frac{x}{6}$$$$\Rightarrow \frac{Green+b}{Majenta+a}=\frac{x}{6}$$$$\Rightarrow \frac{3}{4}=\frac{x}{6}\Rightarrow x=4.5unit$$

Answered by mr W last updated on 07/Jan/24

Commented by mr W last updated on 07/Jan/24

$$\mathrm{\Delta }AFB=\mathrm{\Delta }AEB+magenta$$$$=\mathrm{\Delta }AEB+green$$$$=\mathrm{\Delta }ADB$$$$\Rightarrow DF//AB$$$$\Rightarrow \frac{4}{3}=\frac{6}{x}$$$$\Rightarrow x=\frac{3\times 6}{4}=4.5$$

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