Question-220263

Question Number 220263 by Tawa11 last updated on 10/May/25

Answered by mr W last updated on 10/May/25

$${blue}=\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} ×{red} \\ $$$${pink}={green} \\ $$$${blue}+{pink}+{red}+{green}=\mathrm{24}.\mathrm{5} \\ $$$${blue}+{pink}=\frac{\mathrm{3}}{\mathrm{4}}\left({red}+{green}\right) \\ $$$$\Rightarrow{blue}+{pink}=\frac{\mathrm{3}}{\mathrm{7}}×\mathrm{24}.\mathrm{5}=\mathrm{10}.\mathrm{5} \\ $$$$\Rightarrow{red}+{green}=\frac{\mathrm{4}}{\mathrm{7}}×\mathrm{24}.\mathrm{5}=\mathrm{14} \\ $$$${red}−{blue}=\mathrm{14}−\mathrm{10}.\mathrm{5}=\mathrm{3}.\mathrm{5} \\ $$$$\left[\mathrm{1}−\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} \right]×{red}=\mathrm{3}.\mathrm{5} \\ $$$$\Rightarrow{red}=\frac{\mathrm{16}}{\mathrm{7}}×\mathrm{3}.\mathrm{5}=\mathrm{8}\:{cm}^{\mathrm{2}} \\ $$

Commented by Tawa11 last updated on 10/May/25

$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}. \\ $$

Commented by Tawa11 last updated on 10/May/25

$$\mathrm{Sir},\:\:\:\mathrm{1}\:\:−\:\:\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} \:\:=\:\:\:\frac{\mathrm{7}}{\mathrm{16}} \\ $$

Answered by mr W last updated on 10/May/25

$$\frac{\left(\mathrm{3}+\mathrm{4}\right){h}}{\mathrm{2}}=\mathrm{24}.\mathrm{5}\:\Rightarrow{h}=\mathrm{7} \\ $$$${h}_{{blue}} +{h}_{{red}} ={h} \\ $$$$\frac{{h}_{{blue}} }{{h}_{{red}} }=\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\Rightarrow{h}_{{red}} =\frac{\mathrm{4}}{\mathrm{7}}×{h}=\mathrm{4} \\ $$$${A}_{{red}} =\frac{\mathrm{4}×\mathrm{4}}{\mathrm{2}}=\mathrm{8} \\ $$

Commented by Tawa11 last updated on 10/May/25

$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{I}\:\mathrm{appreciate}. \\ $$

Answered by Spillover last updated on 10/May/25

H=24.5/[(3+4)/2]=7
RedA=4×h/2
h=4/7×H=4
RedA=8

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