The cardboard is a rectangle. The diagonal and the sides form a right triangle. Use the Pythagorean Theorem:

$\displaystyle{{10}}^{{2}}+{{20}}^{{2}}={{c}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle{100}+{400}={{c}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle{500}={{c}}^{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle\sqrt{{500}}={c}\usepackage{cmbright}\Huge\$