Question

The length of a hall is 18 m and its width is 13.5 m. Find the least number of square tiles, each of side 25 cm, required to cover the floor of the hall,

(i) without leaving any margin.

(ii) leaving a margin of width 1.5 m all around. In each case, find the cost of the tiles required at the rate of Rs. 6 per tile.

Answer 1

Length of hall (l)=18 m and breadth (b)=13.5 m

$\therefore$ Area of the floor =l \times b

$=18\times 13.5m^2=243.0m^2$

Side of each square tiles (a)=25 cm

$=\frac{25}{100}=\frac{1}{4}m$

$\therefore$ Area of one tile $=a^2=\frac{1}{4}\times \frac{1}{4}$

$=\frac{1}{16}{m}^2$

No. of tiles required $=243+\frac{1}{16}$

$=\frac{243\times 16}{1}=3888$

Rate of tiles =Rs.6 per tile.

$\therefore$ Total cost =Rs.3888 $\times 6$

=Rs.23328

(ii)Width of margin left in side=1.5 m

$\therefore$ Inner length $=18-2\times 1.5=18-3=15$ m and breadth $=13.5-2\times 1.5=13.5-3=10.5m$

$\therefore$ Inner area $=15\times 10.5m^2=157.5m^2$

$\therefore$ No. of tiles $=157.5+\frac{1}{16}$

$=157.5\times 16=2520$

$\therefore$ Cost of tiles $=2520\times 6$=Rs.15120