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Question-157425




Question Number 157425 by cortano last updated on 23/Oct/21
Answered by mr W last updated on 23/Oct/21
r^2 =(8+r)^2 −(7+r)^2 =15+2r  (r+3)(r−5)=0  ⇒r=5  fraction of shaded area=((r/(8+r)))^2 =((25)/(169))
$${r}^{\mathrm{2}} =\left(\mathrm{8}+{r}\right)^{\mathrm{2}} −\left(\mathrm{7}+{r}\right)^{\mathrm{2}} =\mathrm{15}+\mathrm{2}{r} \\ $$$$\left({r}+\mathrm{3}\right)\left({r}−\mathrm{5}\right)=\mathrm{0} \\ $$$$\Rightarrow{r}=\mathrm{5} \\ $$$${fraction}\:{of}\:{shaded}\:{area}=\left(\frac{{r}}{\mathrm{8}+{r}}\right)^{\mathrm{2}} =\frac{\mathrm{25}}{\mathrm{169}} \\ $$
Commented by Tawa11 last updated on 23/Oct/21
Weldone sir
$$\mathrm{Weldone}\:\mathrm{sir} \\ $$

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