Answer:
ab/(a+b)
Step-by-step explanation:
Without loss of generality, we can put point C at the origin and define line BD by the equation ...
x/a +y/b = 1
Points (x, y) fall on the line BD, and we have point L where x=y. That value of x, the square's side length, will satisfy ...
x/a +x/b = 1 . . . . . fill in x=y in the equation
x(a+b)/ab = 1 . . . .factor out x, add 1/a+1/b
x = ab/(a+b) . . . . solve for x
The length of the side of the square is ab/(a+b).
