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Question-121330




Question Number 121330 by ajfour last updated on 06/Nov/20
Commented by ajfour last updated on 06/Nov/20
Find ratio of coloured area to  outer square area.
$${Find}\:{ratio}\:{of}\:{coloured}\:{area}\:{to} \\ $$$${outer}\:{square}\:{area}. \\ $$
Commented by MJS_new last updated on 06/Nov/20
I think this is not possible in a square???  but I′m tired and maybe I′m wrong...
$$\mathrm{I}\:\mathrm{think}\:\mathrm{this}\:\mathrm{is}\:\mathrm{not}\:\mathrm{possible}\:\mathrm{in}\:\mathrm{a}\:\mathrm{square}??? \\ $$$$\mathrm{but}\:\mathrm{I}'\mathrm{m}\:\mathrm{tired}\:\mathrm{and}\:\mathrm{maybe}\:\mathrm{I}'\mathrm{m}\:\mathrm{wrong}… \\ $$
Answered by mr W last updated on 07/Nov/20
Commented by mr W last updated on 07/Nov/20
tan α=((1−x)/1)=1−x  tan α=((1−y)/1)=1−y  ⇒x=y  ⇒AE=AF  ⇒β=π−2×(π/2)=0  ⇒impossible
$$\mathrm{tan}\:\alpha=\frac{\mathrm{1}−{x}}{\mathrm{1}}=\mathrm{1}−{x} \\ $$$$\mathrm{tan}\:\alpha=\frac{\mathrm{1}−{y}}{\mathrm{1}}=\mathrm{1}−{y} \\ $$$$\Rightarrow{x}={y} \\ $$$$\Rightarrow{AE}={AF} \\ $$$$\Rightarrow\beta=\pi−\mathrm{2}×\frac{\pi}{\mathrm{2}}=\mathrm{0} \\ $$$$\Rightarrow{impossible} \\ $$
Commented by ajfour last updated on 07/Nov/20
thanks for attempting Sir.
$${thanks}\:{for}\:{attempting}\:{Sir}. \\ $$

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