Australian AMC 2017 - Senior Question 21

Question 21

A square is drawn in the corner of a right-angled triangle with side lengths $a,b,c$, as shown. Which expression gives the ratio of the unshaded area to the shaded area in all cases?

Question illustration

$1:1$
$c:(a+b)$
$ab:c^2$
$(a+b)^2:2c^2$
$c^2:2ab$