Question Number 227795 by Tawa11 last updated on 18/Feb/26
Answered by mr W last updated on 18/Feb/26
Commented by mr W last updated on 18/Feb/26
$$\mathrm{8}−{x}=\mathrm{5} \\ $$$$\Rightarrow{x}=\mathrm{3} \\ $$$$\sqrt{{y}}×\sqrt{{x}}=\mathrm{5} \\ $$$$\Rightarrow{y}=\frac{\mathrm{5}^{\mathrm{2}} }{{x}}=\frac{\mathrm{25}}{\mathrm{3}}\:\checkmark \\ $$
Commented by Tawa11 last updated on 21/Feb/26
$$\mathrm{Thanks}\:\mathrm{sir},\:\mathrm{I}\:\mathrm{appreciate} \\ $$
Answered by mahdipoor last updated on 18/Feb/26
$$\mathrm{xy}=\mathrm{5} \\ $$$$\mathrm{XY}=\mathrm{8} \\ $$$$\mathrm{Y}=\mathrm{X}+\mathrm{x}\:\:\left(\mathrm{ABCD}\right) \\ $$$$\mathrm{x}=\mathrm{Y}−\mathrm{y}\:\:\:\left(\mathrm{red}\:\mathrm{sq}\right) \\ $$$$\Rightarrow\mathrm{X}=\mathrm{y}\Rightarrow\mathrm{Xx}=\mathrm{5}\:,\:\mathrm{X}\left(\mathrm{X}+\mathrm{x}\right)=\mathrm{8} \\ $$$$\mathrm{x}=\sqrt{\frac{\mathrm{25}}{\mathrm{3}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{X}=\frac{\mathrm{3}}{\mathrm{5}}\sqrt{\frac{\mathrm{25}}{\mathrm{3}}}\:\:\:\: \\ $$$$\mathrm{y}=\frac{\mathrm{3}}{\mathrm{5}}\sqrt{\frac{\mathrm{25}}{\mathrm{3}}}\:\:\:\:\:\:\:\:\mathrm{Y}=\frac{\mathrm{8}}{\mathrm{5}}\sqrt{\frac{\mathrm{25}}{\mathrm{3}}} \\ $$$$\Rightarrow\mathrm{red}\:\mathrm{sq}\:=\:\left(\mathrm{Y}−\mathrm{y}\right)\mathrm{x}=\mathrm{x}^{\mathrm{2}} =\frac{\mathrm{25}}{\mathrm{3}} \\ $$
Commented by Tawa11 last updated on 21/Feb/26
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$$$\mathrm{I}\:\mathrm{appreciate}. \\ $$