Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110cm b

Question

Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110cm by 130cm such that the tiles donot overlap. A tile can b 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. The maximum number of tiles that can b accomodated on the floor is
(a) 4
(b) 5
(c) 6
(d) 7
The answer is 6 but how?

Answer 1

Each letter represents a 10cm X 10cm square. A, B, C, D, E, and F represent the 6 different 70cm X 30cm tiles. S represents a space not covered by tiles.


AAASBBBBBBB
AAASBBBBBBB
AAASBBBBBBB
AAASCCCCCCC
AAASCCCCCCC
AAASCCCCCCC
AAASSSSSDDD
EEEEEEESDDD
EEEEEEESDDD
EEEEEEESDDD
FFFFFFFSDDD
FFFFFFFSDDD
FFFFFFFSDDD

Answer 2

If As, Bs, Cs, Ds, Es, and Fs are the area covered by the 6 tiles, and Zs are the empty area, and each letter represents an area of 10cm2 x 10cm2, then it should be something like...

S S S S S S S A A A B B B
C C C C C C C A A A B B B
C C C C C C C A A A B B B
C C C C C C C A A A B B B
D D D E E E S A A A B B B
D D D E E E S A A A B B B
D D D E E E S A A A B B B
D D D E E E F..F.F..F. F .F. F
D D D E E E F..F.F..F. F .F. F
D D D E E E F..F.F..F. F .F. F
D D D E E E S S S S S S S
this!

Answer 3

The area of the Floor = 110 X 130 = 14300 cm2

The area of the tiles that need to be placed = 70 X 30 = 2100 cm2

Therefore, Maximum amount of tiles which can be placed = 14300 / 2100
=6.81

As you cannot place half tiles or more than 6.81 files thus the max number of tiles which can be arranged is c) 6