Question

Diagonal of a square is 4 root 2. Find the length of a side of a square

Answer 1

Check the picture below.

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{4√(2)}\\ a=\stackrel{adjacent}{s}\\ b=\stackrel{opposite}{s}\\ \end{cases}\implies (4√(2))^2~~ = ~~s^2~~ + ~~s^2 \\\\\\ 4^2√(2^2)~~ = ~~2s^2\implies 16(2)=2s^2\implies 32=2s^2\implies \cfrac{32}{2}=s^2 \\\\\\ 16=s^2\implies √(16)=s\implies \boxed{4=s}`