Question

. A floor which measures 15 mx 8 m to be laid with tiles measuring 50 cm by 25 cm Find the number
of tiles required. Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges
and the edges of the floor, what fraction of the floor is uncovered?
​

Answer 1

Step-by-step explanation:

We know, 50cm=0.5m and 

25cm=0.25m

Tiles along the length of the room=0.5/15

                                                      =30 tiles

Tiles along the length of the room=0.2/58

                                                      =32 tiles

Total number of tiles required       =30×32

                                                      =960 tiles

To leave 1m between the carpet and wall on all sides, the carpet needs to be 2m shorter in each dimension.

Therefore,

  (15−2)m(8−2)m

=(13×6)m

=78m2

Therefore, the room area is 15×8

                            =120m2

The carpet area is 78m2

The fraction of the area uncovered is

                             =120/120−78

                             =120/42

                             =20/7                          

Answer 2

Consider ABCD as a rectangular field of measurement 15m × 8m

Length = 15 m

Breadth = 8 m

Here the area = l × b = 15 × 8 = 120 m2

Measurement of tiles = 50 cm × 25 cm

Length = 50 cm = 50/100 = ½ m

Breadth = 25 cm = 25/100 = ¼ m

So the area of one tile = ½ × ¼ = 1/8 m2

No. of required tiles = Area of rectangular field/Area of one tile

Substituting the values

= 120/ (1/8)

By further calculation

= (120 × 8)/ 1

= 960 tiles

Length of carpet = 15 – 1 – 1

= 15 – 2

= 13 m

Breadth of carpet = 8 – 1 – 1

= 8 – 2

= 6 m

Area of carpet = l × b

= 13 × 6

= 78 m2

We know that

Area of floor which is uncovered by carpet = Area of floor – Area of carpet

Substituting the values

= 120 – 78

= 42 m2

Fraction = Area of floor which is uncovered by carpet/ Area of floor

Substituting the values

= 42/120

= 7/20

${\fcolorbox{blue}{black}{\blue{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:HumanIntelligence\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$