Question Number 208148 by Blackpanther last updated on 06/Jun/24
Answered by A5T last updated on 06/Jun/24
Commented by A5T last updated on 06/Jun/24
![2y=6x⇒y=3x ⇒15^2 =(3y)^2 +y^2 =10y^2 ⇒y^2 =((225)/(10))=((45)/2) ⇒[Blue square]=(2y)^2 =4y^2 =4×((45)/2)=90](Q208151.png)
$$\mathrm{2}{y}=\mathrm{6}{x}\Rightarrow{y}=\mathrm{3}{x} \\ $$$$\Rightarrow\mathrm{15}^{\mathrm{2}} =\left(\mathrm{3}{y}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{10}{y}^{\mathrm{2}} \Rightarrow{y}^{\mathrm{2}} =\frac{\mathrm{225}}{\mathrm{10}}=\frac{\mathrm{45}}{\mathrm{2}} \\ $$$$\Rightarrow\left[{Blue}\:{square}\right]=\left(\mathrm{2}{y}\right)^{\mathrm{2}} =\mathrm{4}{y}^{\mathrm{2}} =\mathrm{4}×\frac{\mathrm{45}}{\mathrm{2}}=\mathrm{90} \\ $$
Answered by mr W last updated on 06/Jun/24
Commented by mr W last updated on 06/Jun/24
$$\frac{\mathrm{15}}{{a}}=\frac{\mathrm{5}}{\:\sqrt{\mathrm{5}^{\mathrm{2}} −{a}^{\mathrm{2}} }}\:\Rightarrow{a}^{\mathrm{2}} =\frac{\mathrm{45}}{\mathrm{2}} \\ $$$${colored}\:{area}\:=\left(\mathrm{2}{a}\right)^{\mathrm{2}} =\mathrm{4}×\frac{\mathrm{45}}{\mathrm{2}}=\mathrm{90} \\ $$
Commented by Tawa11 last updated on 21/Jun/24
$$\mathrm{learning}\:\mathrm{sir} \\ $$