SOLUTION —
Eccentricity of rectangular hyperbola $=\sqrt{2}$
$\therefore$ Distance between directrices $=\frac{2 a}{\sqrt{2}}$
From the given condition,
$\begin{array}{l}\frac{2 a}{\sqrt{2}}=10 \\\Rightarrow \quad 2 a=10 \sqrt{2} \\\end{array}$
Distance between foci $=2 \alpha e=10 \sqrt{2} \cdot \sqrt{2}=20$
So, The correct option of this question will be (D).