Question Number 203969 by mr W last updated on 03/Feb/24
Answered by Rasheed.Sindhi last updated on 03/Feb/24
$$?={x} \\ $$$$\bigtriangleup\mathrm{ABC}\sim\bigtriangleup\mathrm{ADE} \\ $$$$\frac{\mathrm{3}}{{r}}=\frac{\mathrm{4}}{\mathrm{4}−{r}}=\frac{\mathrm{5}}{{x}+{r}}\Rightarrow\mathrm{4}{r}=\mathrm{12}−\mathrm{3}{r}\Rightarrow{r}=\frac{\mathrm{12}}{\mathrm{7}} \\ $$$$\frac{\mathrm{3}}{{r}}=\frac{\mathrm{5}}{{x}+{r}}\Rightarrow\frac{\mathrm{3}}{\frac{\mathrm{12}}{\mathrm{7}}}=\frac{\mathrm{5}}{{x}+\frac{\mathrm{12}}{\mathrm{7}}} \\ $$$$\mathrm{3}{x}+\frac{\mathrm{36}}{\mathrm{7}}=\frac{\mathrm{60}}{\mathrm{7}} \\ $$$$\mathrm{3}{x}=\frac{\mathrm{60}−\mathrm{36}}{\mathrm{7}} \\ $$$${x}=\frac{\mathrm{8}}{\mathrm{7}} \\ $$$$ \\ $$
Commented by Rasheed.Sindhi last updated on 03/Feb/24
Commented by mr W last updated on 03/Feb/24
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