Question Number 194861 by cherokeesay last updated on 17/Jul/23
Answered by horsebrand11 last updated on 17/Jul/23
$$\:\:\mathrm{let}\:\mathrm{the}\:\mathrm{side}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{small} \\ $$$$\:\:\mathrm{square}\:\mathrm{be}\:\mathrm{p}. \\ $$$$\:\:\left(\mathrm{1}+\mathrm{p}\right)^{\mathrm{2}} \:+\:\mathrm{p}^{\mathrm{2}} \:=\:\left(\sqrt{\mathrm{2}}\:\right)^{\mathrm{2}} \\ $$$$\:\:\mathrm{2p}^{\mathrm{2}} +\mathrm{2p}−\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\mathrm{p}=\:\frac{\sqrt{\mathrm{3}}−\mathrm{1}}{\mathrm{2}} \\ $$$$\:\:\:\cancel{\underline{\underbrace{\:}}} \\ $$