8. A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the nan leaving all around a margin of 75 cm from the walls. Find the area of the carpet and the area ot the strip left uncovered. If the width of the carpet is 82 cm, find its cost at the rate ot Rs.60 per m.
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Answer:
In rectangular hall,
Length
(
L
)
=
22
m
Breadth
(
B
)
=
15.5
m
The area of the hall
=
L
×
B
=
22
m
×
15.5
m
=
341
m
2
Margin of carpet
=
75
c
m
=
0.75
m
In carpet,
Length
(
l
)
=
22
m
−
2
×
0.75
m
=
22
m
−
1.5
m
=
20.5
m
Breadth
(
b
)
=
15.5
m
−
2
×
0.75
m
=
15.5
m
−
1.5
m
=
14
m
Area of the carpet
=
l
×
b
=
20.5
m
×
14
m
=
287
m
2
Area of uncovered portion
=
3341
m
2
−
287
m
2
=
54
m
2
Now, it is given that width of the carpet
=
82
c
m
=
0.82
m
Since, Area of the carpet
=
287
m
2
⇒
l
×
b
=
287
m
2
⇒
l
×
0.82
m
=
287
m
2
⇒
l
=
287
m
2
0.82
m
⇒
l
=
287
×
100
82
m
⇒
l
=
350
m
Cost of the carpet per meter
=
R
s
.
60
Cost of fencing the strip
=
350
×
R
s
.
60
=
R
s
.21000
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