The following question was asked in a competitive exam
Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor.What is the maximum number of tiles that can be accommodated on the floor ?
Solution obtained by trial and error. answer from above diagram is 6 .
but is there a equation or inequality based approach (because I cannot rely on trial and error) like $$130*110 - 70*30*n < 70*30 $$ $$ n >5.8 $$ so n is the next integer so 6 , so we might get the answer right , but is the approach right ? for example if it is some other shape which is also of area $130\times110 = 14300$ but not a rectangle ,there is no guaranty that we can place inside it 6 smaller tiles.so this approach is not applicable at all places .
so guide me in knowing the right approach . please help . I am stuck .