Question Number 182091 by mr W last updated on 04/Dec/22
Commented by mr W last updated on 04/Dec/22
$${the}\:{areas}\:{of}\:{three}\:{squares}\:{are}\:{given}. \\ $$$${find}\:{the}\:{sum}\:{of}\:{the}\:{areas}\:{of}\:{the}\:{other} \\ $$$${four}\:{squares}. \\ $$
Answered by JDamian last updated on 04/Dec/22
$$\mathrm{8} \\ $$$${S}_{{k}} \:{and}\:{S}_{{k}+\mathrm{1}} \:{are}\:{related}\:{by}\:{Pythagorean} \\ $$$${theorem}: \\ $$$$ \\ $$$${S}_{\mathrm{1}} +{S}_{\mathrm{2}} =\mathrm{3}\:\:\left({i}\right) \\ $$$${S}_{\mathrm{2}} +{S}_{\mathrm{3}} =\mathrm{4} \\ $$$${S}_{\mathrm{3}} +{S}_{\mathrm{4}} =\mathrm{5}\:\left({ii}\right) \\ $$$$ \\ $$$${i}\:+\:{ii}\:\:\:=\:\:\:{S}_{\mathrm{1}} +{S}_{\mathrm{2}} +{S}_{\mathrm{3}} +{S}_{\mathrm{4}} =\mathrm{3}+\mathrm{5}=\mathrm{8} \\ $$
Commented by mr W last updated on 04/Dec/22
$${thanks}! \\ $$$${nice}\:{solution}! \\ $$$${following}\:{diagram}\:{gives}\:{some}\:{more} \\ $$$${explanation}. \\ $$
Commented by mr W last updated on 04/Dec/22
Commented by mr W last updated on 04/Dec/22
$${c}^{\mathrm{2}} ={a}^{\mathrm{2}} +{b}^{\mathrm{2}} \\ $$$$\Rightarrow{A}_{\mathrm{1}} ={A}_{\mathrm{2}} +{A}_{\mathrm{3}} \\ $$