There are two answers to this problem: a 6 x 3 rectangle (having a perimeter and area of 18) and a 10 x 2.5 rectangle (having a perimeter and area of 25).
In computational geometry, the largest empty rectangle problem, maximal empty rectangle problem or maximum empty rectangle problem, is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There are a number of variants of the problem, depending on the particularities of this generic formulation, in particular, depending on the measure of the "size", domain (type of obstacles), and the orientation of the rectangle.
The problems of this kind arise e.g., in electronic design automation, in design and verification of physical layout of integrated circuits. R-tree