How do I find the hypotenuse of a right triangle if the leg is a variable and the base is made up of the same variable*2?

Question

The question says: 

A rectangle of side length s and a width of 2s is cut along its diagonal into 2 smaller pieces. One of the two pieces is cut along the median of the right angle. Find the perimeter of the larger of the two pieces in terms of s. 

Answer 1

The median of the triangle's right angle is defined to be the segment from the right angle vertex to the midpoint of the side opposite the right angle. 

 

If we draw both diagonals of the rectangle, they bisect each other by symmetry. Therefore the median of the right angle in question is equal in length to one-half the hypotenuse of the right triangle it belongs to (which was defined to be one half the rectangle).

 

All told we have a perimeter of s + s √5 = s(1 + √5)