#### Answer

$x =10\sqrt{2}+10 \approx 24.1$

#### Work Step by Step

Cross Multiply:
$\frac{5\sqrt{2}}{\sqrt{2}-1}=\frac{x}{\sqrt{2}},
5\sqrt{2}\sqrt{2}=x(\sqrt{2}-1)
, 10=x(\sqrt{2}-1)
, x=\frac{10}{\sqrt{2}-1}\cdot \frac{\sqrt{2}+1}{\sqrt{2}+1}= \frac{10\sqrt{2}+10}{2-1}=10\sqrt{2}+10$