Question

The floor of a room is 6 m 50 cm long and 5 m 25 cm wide. It is to be paved by equal square marble tiles. Find the largest size of the tile and hence find the least number of tiles required.​

Answer 1

Area of floor = 36×24=864 sq. m

Area of one tile = 6×6=36 sq. m.

Therefore,

Tiles required =

36

864

=24 tiles

Answer 2

Step-by-step explanation:

Length of floor = 6 m 50 cm = 650 cm

Width of floor = 5 m 25 cm = 525 cm

To find the maximum size of the tile, we need to find HCF of the dimensions of the floor.

$:\longmapsto$ 650 = 2 × 5² × 13

$:\longmapsto$ 525 = 3 × 5² × 7

$:\longmapsto$ HCF(650, 525) = 5² = 25

Hence, the largest size of square tile is 25 × 25 (in cm)

$\color{#FF7968}{\rule{36pt}{7pt}}\color{#FEDD8E}{\rule{36pt}{7pt}}\color{#FBBE2E}{\rule{36pt}{7pt}}\color{#60D399}{\rule{36pt}{7pt}}\color{#6D83F3}{\rule{36pt}{7pt}}$

Now , the floor is a rectangle whose area is,

$\boxed{\boxed{\tt \bf Area \ of \ Rectangle = Length \times width}}$

Thus,

$:\longmapsto$ area of floor = 650 cm × 525 cm = 341250 cm²

Now , the marble tiles are square. Area of square is given by,

$\boxed{\boxed{\tt \bf Area \ of \ Square = (side)^2}}$

Thus,

$:\longmapsto$ Area of each tile = (25)² = 625 cm²

Thus,

$:\longmapsto$The number of tiles = $\sf \dfrac{Area \ of \ floor}{Area \ of \ tile}$

$:\longmapsto$ Number of tiles = $\sf \dfrac{341250\ cm^2}{625 \ cm^2}$

$:\longmapsto$ Number of tiles = 546

Hence the number of tiles is 546

$\color{#FF7968}{\rule{36pt}{7pt}}\color{#FEDD8E}{\rule{36pt}{7pt}}\color{#FBBE2E}{\rule{36pt}{7pt}}\color{#60D399}{\rule{36pt}{7pt}}\color{#6D83F3}{\rule{36pt}{7pt}}$