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Question-201853




Question Number 201853 by sonukgindia last updated on 14/Dec/23
Answered by AST last updated on 14/Dec/23
Let green segment=g;orange segment=r  and blue segment=b;side of square=s  (b/r)=((7−5)/(7−3))⇒r=2b;(g/(g+s))=(2/4)⇒g=s  ((2b)/(2b+s))=((7−3)/(13−3))=(2/5)⇒5r=2r+2s⇒r=((2s)/3)  r^2 +(s+g)^2 =16⇒((4s^2 )/9)+4s^2 =16⇒40s^2 =16×9  ⇒s^2 =((4×9)/(10))=3.6
$${Let}\:{green}\:{segment}={g};{orange}\:{segment}={r} \\ $$$${and}\:{blue}\:{segment}={b};{side}\:{of}\:{square}={s} \\ $$$$\frac{{b}}{{r}}=\frac{\mathrm{7}−\mathrm{5}}{\mathrm{7}−\mathrm{3}}\Rightarrow{r}=\mathrm{2}{b};\frac{{g}}{{g}+{s}}=\frac{\mathrm{2}}{\mathrm{4}}\Rightarrow{g}={s} \\ $$$$\frac{\mathrm{2}{b}}{\mathrm{2}{b}+{s}}=\frac{\mathrm{7}−\mathrm{3}}{\mathrm{13}−\mathrm{3}}=\frac{\mathrm{2}}{\mathrm{5}}\Rightarrow\mathrm{5}{r}=\mathrm{2}{r}+\mathrm{2}{s}\Rightarrow{r}=\frac{\mathrm{2}{s}}{\mathrm{3}} \\ $$$${r}^{\mathrm{2}} +\left({s}+{g}\right)^{\mathrm{2}} =\mathrm{16}\Rightarrow\frac{\mathrm{4}{s}^{\mathrm{2}} }{\mathrm{9}}+\mathrm{4}{s}^{\mathrm{2}} =\mathrm{16}\Rightarrow\mathrm{40}{s}^{\mathrm{2}} =\mathrm{16}×\mathrm{9} \\ $$$$\Rightarrow{s}^{\mathrm{2}} =\frac{\mathrm{4}×\mathrm{9}}{\mathrm{10}}=\mathrm{3}.\mathrm{6} \\ $$

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