Given three squares as in the figure, where the largest square has area 1, and the area A is known. What is the area B of the smallest square.
Upon lookin at the answer for this excercise, I found the following reasoning as part of the solution:
Let the corner of A divide the sides of the big square in two parts x and 1-x. square B have side-length y. For the corner of B to touch the side of A, we must have y/x + y/(1-x) = 1 (the equation for a line)
I do not understand anything about the part with the line-equation, but this seems like a powerful tool i shall have use of knowing. Could someone please explain this for me?