complexity theory - how to justify that "Tile Cover" is in NP -

hi im learning exam in theoretical computer science. , im learning exams of last years because task setting similar every year. , can solve of tasks except of one: there 1 question "p vs. np" problem.

an example of lat year:

we have given "tile cover" problem witch says: have "big" rectangle page length of n x m ∈ n , have k "small" rectangles ("tiles") r1, r2, ..., rk

the question if "small" rectangles fit in "big" 1 without leaving space on it.

and ther tasks problem , despair on first 1 witch says:

"justify informal why 'tile cover' problem in np"

how solve problem, or similar 1 (bacause dont think same in year)

recall well-known characterization of complexity class np says np comprised of precisely problems which, given problem instance i , certificate c(i), can verify in polynomial time instance i has solution (using certificate, of 1 can think of hint algorithm). more concretely, 1 can think of certificate solution problem instance (although it's more general that). (the proof of theorem formalizing claim can found in superb book sanjeev arora , boaz barak.)

thus show problem in np suffices prove that, given solution problem instance, can verify in time polynomial in size of solution , size of problem solution indeed valid.

for specific case, suffices show if given rectangle r , set of "small" rectangles s, , solution problem---a tiling of r tiles s---, there algorithm verifies tiling (or valid or whatever call it) in polynomial time.