Question

$\huge\sf{Question}$
A rectangular floor which measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 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?

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Answer 1

Answer:

$\frac{7}{20}$

Step-by-step explanation:

50cm

First we will convert it to m

$\frac{50}{100} \\ \\ = 0.5m$

25 cm

$= \frac{25}{100} \\ \\ = 0.25m$

Tiles along the length of the room=

$\frac{ = 15}{0.5} \\ \\ = 30tiles$

Tiles along the length of the room=

$\frac{8}{0.25} = 32tiles$

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.

so

$(15 - 2)m(8 - 2)m \\ \\ = (13 \times 6)m \\ \\ = {78m}^{2}$

So area of room

$= 15 \times 8 = {120m}^{2}$

Fraction of the area which is uncovered

$= \frac{120 - 78}{120} \\ \\ = \frac{ \cancel{ {42}} \: \: ^{7} }{ \cancel{120} \: \: ^{20} } \\ \\ = \frac{7}{20}$

Hope it helps you from my side

Answer 2

answer :

$= \frac{7}{20}$

steps :

We know, 50cm=0.5m and

25cm=0.25m

Tiles along the length of the room=

$\frac{15}{0.5} \\ = 30 \: tiles</p><p></p><p>$

Tiles along the length of the room =

$\frac{8}{0.25} \\ = 32tiles$

Total number of tiles required

$=30×32 =960 tiles</p><p></p><p>$

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

Therefore,

$\: (15−2)m(8−2)m \\ </p><p>=(13×6)m$

$= 78 {m}^{2}$

Therefore, the room area is

$15 \times 8 \\ = {120}^{2}$

the carpet area is

${78}^{2}$

The fraction of the area uncovered =

$\frac{120 - 78}{120} \\ = \frac{42}{120} \\ = \frac{7}{20}$