Here is a before and after drawing of the scenario:
The question is what is y?
First we can solve for x.
Use Pythagorean Theorem.
x2 + 202 = 252
x = 15
Now use this info about x to solve for y with Pythagorean Theorem..
(15 - 2y)2 + (20 + y)2 = 252
Multiply this out.
(15 - 2y)(15 - 2y) + (20 + y)(20 + y) = 625
225 - 60y + 4y2 + 400 + 40y + y2 = 625
Combine like terms and write in descending order.
5y2 - 20y + 625 = 625
5y2 - 20y = 0
Divide everything by 5.
y2 - 4y = 0
Factor.
(y)(y-4) = 0
Set each factor equal to zero and solve for y.
Either y = 0 or y = 4
It doesn't make sense for y to be 0, if y was 0, it would be the exact same triangle we started with!
y = 4 feet