A scenery in your drawing room has height h and is hung in the wall so that its lower edge is at a distance d above the eye of an observer. How far from the wall should the observer stand to get the best view?

To determine the optimal viewing distance, we need to consider the relationship between the height of the scenery (h), the distance of the lower edge from the eye (d), and the viewing distance from the wall (x).

Let's assume that the observer's eye is at a height "e" from the ground. Now, consider the triangle formed by the observer's eye, the lower edge of the scenery, and the top edge of the scenery when viewed from a side perspective.

In this triangle, the height of the scenery (h) forms the vertical side, the distance from the lower edge to the observer's eye (d) forms the horizontal side, and the viewing distance from the wall (x) forms the hypotenuse.

Using similar triangles, we can establish the following relationship:

h / (x - d) = e / x

To find the optimal viewing distance (x), we can rearrange the equation:

x = (d * e) / (e - h)

Now, by substituting the known values of h and d, we can obtain the optimal viewing distance (x).

It's important to note that the result may vary depending on the specific measurements of h, d, and the observer's eye height (e).