so.. notice the ratios there, those ratios are good, when the triangle is made up of, two 45 degree angles, and one 90 thus is called a 45-45-90 angle
the two legs are the same length and the hypotenuse, or longest leg, whatever the others are, times square root of 2
so.. one could say that [tex]\bf 16=x\sqrt{2}\implies \cfrac{16}{\sqrt{2}}=x
\\ \quad \\
\textit{now, we could rationalize that by}
\\ \quad \\
\cfrac{16}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}=x\implies \cfrac{16\sqrt{2}}{(\sqrt{2})^2}=x\implies \cfrac{16\sqrt{2}}{2}=x\implies 8\sqrt{2}=x[/tex]
