What is the distance between the top of the box and the top of the ladder?

Question

A cubical box is placed along a wall, and a ladder leans against the wall so it just touches the corner of the box, as shown below.

If the ladder’s length is 4, and the box has a side of 1, what is the distance between the top of the box and the top of the ladder?

Answer 1

Let X = ? and Y the distance between the cube and the ladder at the base
We can write the following equarions,

1 / (1 + X) = Y / ( 1+ Y)
(X + 1)^2 + (Y * 1)^2 = 4^2
By solving the equations
X = 2,78