Question

HELP ASAP!!! Find the length of side x in simplest radical form with a rational denominator.

Answer 1

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{1}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{x} \end{cases} \\\\\\ (1)^2= (x)^2 + (x)^2\implies 1=2x^2\implies \cfrac{1}{2}=x^2\implies \sqrt{\cfrac{1}{2}}=x \\\\\\ \cfrac{1}{√(2)}=x\implies \cfrac{1}{√(2)}\cdot \cfrac{√(2)}{√(2)}=x\implies \cfrac{√(2)}{2}=x`