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Question Number 154138 by iloveisrael last updated on 14/Sep/21

Answered by EDWIN88 last updated on 14/Sep/21

Commented by EDWIN88 last updated on 14/Sep/21

⇒Red area = (1/2)×((18)/7)×((24)/7)=((216)/(49))  (•) (h/6)=((8−2R)/8)  ⇒(h/3)=((4−((24)/7))/2) ; h=((3((4/7)))/2)=(6/7)  ⇒orange area = (1/2)×(8−((24)/7))×(((24)/7))−(1/2)×(8−((24)/7))×(6/7)  orange area =(1/2)×((32)/7)(((24)/7)−(6/7))  orange area = ((16)/7)×((18)/( 7))=((288)/(49))  then ((red area)/(orange area))=((216)/(49))×((49)/(288))=(3/4)

$$\Rightarrow{Red}\:{area}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{18}}{\mathrm{7}}×\frac{\mathrm{24}}{\mathrm{7}}=\frac{\mathrm{216}}{\mathrm{49}} \\ $$$$\left(\bullet\right)\:\frac{{h}}{\mathrm{6}}=\frac{\mathrm{8}−\mathrm{2}{R}}{\mathrm{8}} \\ $$$$\Rightarrow\frac{{h}}{\mathrm{3}}=\frac{\mathrm{4}−\frac{\mathrm{24}}{\mathrm{7}}}{\mathrm{2}}\:;\:{h}=\frac{\mathrm{3}\left(\frac{\mathrm{4}}{\mathrm{7}}\right)}{\mathrm{2}}=\frac{\mathrm{6}}{\mathrm{7}} \\ $$$$\Rightarrow{orange}\:{area}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{8}−\frac{\mathrm{24}}{\mathrm{7}}\right)×\left(\frac{\mathrm{24}}{\mathrm{7}}\right)−\frac{\mathrm{1}}{\mathrm{2}}×\left(\mathrm{8}−\frac{\mathrm{24}}{\mathrm{7}}\right)×\frac{\mathrm{6}}{\mathrm{7}} \\ $$$${orange}\:{area}\:=\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{32}}{\mathrm{7}}\left(\frac{\mathrm{24}}{\mathrm{7}}−\frac{\mathrm{6}}{\mathrm{7}}\right) \\ $$$${orange}\:{area}\:=\:\frac{\mathrm{16}}{\mathrm{7}}×\frac{\mathrm{18}}{\:\mathrm{7}}=\frac{\mathrm{288}}{\mathrm{49}} \\ $$$${then}\:\frac{{red}\:{area}}{{orange}\:{area}}=\frac{\mathrm{216}}{\mathrm{49}}×\frac{\mathrm{49}}{\mathrm{288}}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$

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