I’m having trouble working out how to algebraically get to the answer of this question. (See original image below.)
A square is drawn in the corner of a right-angled triangle with side lengths $a$, $b$, and [hypotenuse] $c$, as shown.
Which expression gives the ratio of the unshaded area [inside the triangle, but outside the square] to the shaded area [of the square] in all cases?
- (A) $1:1$
- (B) $c:(a+b)$
- (C) $a b: c^2$
- (D) $( a + b )^2 : 2 c^2$
- (E) $c^2 : 2 a b$
Apparently the answer is $c^2 : 2 a b$ (choice E), but how?
Your help is greatly appreciated! Thank you in advance.
(Please ignore the pen marks! They are incorrect assumptions a friend made on the diagram.)