Pythagorean Theorem

Use the areas to find the length of the sides of the squares. This would result in the green square having a side length of 3 and the yellow square having a side length of 4. Next add all three sides of the squares: 3 + 4 + 3 = 10. Now you know the length and height of the three squares stacked together. Next, plug in your value of 10 for the a and b variables in the pythagorean theorem equation: $a^2 +b^2 =c^2$ .  $10^2 + 10^2 = c^2$

$100 + 100 = c^2$

$200 = c^2$

$\sqrt{200}$ =c

Using this $If~a~square~has~a~side~length~of~x,~its~diagonal~has~a~length~of~x\sqrt{2}$ So, the length of the line is $3\sqrt{2}+4\sqrt{2}+3\sqrt{2}=10\sqrt{2}=\boxed{\sqrt{200}}$