Can you tell the actual size of an object in a photo by just measuring the image (with some reference objects)? For example, you took a photo of the surface of a table, which is a rectangle. You also know the length of the table, say 50 inches. In the photo, the surface appears as a trapezoid (whose parallel sides correspond to the table's length). Can you calculate the width of the table by just measuring the trapezoid (angle, length etc)?
You don't know the focal length and the object distance.
 A: I think this is really a math question (3D geometry) rather than physics. The topic is projective geometry. Making measurements from photographs is photogrammetry. 
This question has been asked in Mathematics SE, for example Calculate real length of object from perspective image- width of building and How can I figure out the length of a rectangle when I know the width of it. In both cases the OP like you is trying to find the unknown side of a rectangle. 
In both cases the answer is No. Lee Mosher's answer to the 2nd question is that with a suitable choice of observer/camera position the images of any two  rectangles can be made congruent. The same is in fact true for all triangles, all parallelograms (but not all quadrilaterals), and also for all ellipses. These classes of planar figure are projectively equivalent. See What classes of polygons are equivalent up to affine transformation?
Knowing that the object is a rectangle (not a trapezium or parallelogram) is not enough. Some other information is required. MvG's more detailed answer to the 1st question says

As a general rule, if you know the relative positions of any four non-colinear points in a single object plane then you can compute the transformation matrix and apply its inverse to un-project that plane and read any other dimensions from the image plane.

You can do the same with 3 points on the object line, to find any distances in the object from it image line.
You know the relative positions of 2 points in the object plane (the table). Knowing that the table is rectangular is equivalent to having one other point, so knowing the relative position of a 3rd point on the table (not on the known edge) would enable you to find the length of the unknown side.
Alternatively, knowing the position of the camera relative to plane of the table would enable you to do the calculation. 
A: There is an extra parameter to consider and that is the "height" of the camera above the object.  

