#### Answer

20.8

#### Work Step by Step

$12^2+x^2=24^2$
$144+x^2=576$
$x^2=432$
$\sqrt {432}=x$
$\sqrt {432}\approx20$
Divide and average to refine the approximation.
$432\div20=21.6$
$(20+21.6)\div2=20.8$
Repeat to further refine.
$432\div20.8=20.77$
$(20.8+20.77)\div2=20.785$