Question

Please show me how you find x and determine what x is
Thank you I appreciate it :)

Answer 1

well, let's notice something, we have two 45° angles, now each of those will give use an equal opposite side, namely if that one side is "x", the other is her twin, "x" as well.

is a right-triangle, so we can use the pythagorean theorem, and we know the sides are x,x,6.

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies 6^2=x^2+x^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{6}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{x}\\ \end{cases} \\\\\\ 36=2x^2\implies \cfrac{36}{2}=x^2\implies 18=x^2\implies √(18)=x\implies √(9\cdot 2)=x \\\\\\ √(3^2\cdot 2)=x\implies \boxed{3√(2)=x}`