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Question Number 186359 by normans last updated on 03/Feb/23

Answered by HeferH last updated on 03/Feb/23

Commented by HeferH last updated on 03/Feb/23

$$i.\frac{x+A}{2B+\frac{3A}{2}}=\frac{2}{3}$$$$3x+3A=4B+3A$$$$B=\frac{3x}{4}$$$$ii.\frac{\frac{5A}{2}+\frac{3x}{4}+7}{x+A-14}=\frac{5}{2}$$$$5A+\frac{3x}{2}+14=5x+5A-70$$$$\frac{3x}{2}+14=5x-70$$$$3x+28=10x-140$$$$168=7x$$$$x=24$$

Commented by normans last updated on 03/Feb/23

$$\mathit{v}\mathit{e}\mathit{r}\mathit{y}\mathit{n}\mathit{i}\mathit{c}\mathit{e}\mathit{S}\mathit{i}\mathit{r}$$

Answered by mr W last updated on 05/Feb/23

Commented by mr W last updated on 05/Feb/23

$$CD=\frac{1}{2}\times GH=\frac{1}{2}\times \frac{2}{7}\times AD=\frac{1}{7}\times AD$$$$BD=\frac{5}{7}\times EF=\frac{5}{7}\times \frac{5}{7}\times AD=\frac{25}{49}\times AD$$$$AB=AD-BD=(1-\frac{25}{49})\times AD=\frac{24}{49}\times AD$$$$\frac{x}{7}=\frac{AB}{CD}=\frac{24}{49}\times \frac{7}{1}=\frac{24}{7}$$$$\Rightarrow x=24✓$$

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