Question 8
(FRA 2) Let $R$ be a rectangle that is the union of a finite number of rectangles $R_i$, $1\le i\le n$, satisfying the following conditions:
(i) The sides of every rectangle $R_i$ are parallel to the sides of $R$.
(ii) The interiors of any two different $R_i$ are disjoint.
(iii) Every $R_i$ has at least one side of integral length.
Prove that $R$ has at least one side of integral length.
(i) The sides of every rectangle $R_i$ are parallel to the sides of $R$.
(ii) The interiors of any two different $R_i$ are disjoint.
(iii) Every $R_i$ has at least one side of integral length.
Prove that $R$ has at least one side of integral length.