The length of a room is 50 per cent more than its breadth
The cost of carpeting the room at athe rate of 38.50m2 is
₹924 and the cost of painting the walls at the rate of 5.5
per
m2 is 1,320. Find the dimensions of the room.
Answers
Step-by-step explanation:
Let,
the breadth of the room be \bf{b}b m.
According to the question,
the length of the room is 50% more than its breadth.
length \bf{(l)}(l) = \bf{b}b + 50% of \bf{b}b
length \bf{(l) }(l) = \bf{b}b + \frac{50}{100}
100
50
× \bf{b}b
length \bf{(l) }(l) = \bf{b}b + \frac{b}{2}
2
b
length \bf{(l) }(l) = \frac{3b}{2}
2
3b
Now,
Area of the floor = \frac{924}{38.50}
38.50
924
[ as the cost of carpeting the room at the rate of ₹ 38.50 m² is ₹ 924 ]
=> Area of the floor = 924 ÷ \frac{3850}{100}
100
3850
=> length × breadth = 924 × \frac{100}{3850}
3850
100
=> \frac{3b}{2}
2
3b
× b = 24
=> \frac{3 {b}^{2} }{2} = 24
=> 3b² = 24 × 2
=> 3b² = 48
=> b² = \frac{48}{3}
3
48
=> b² = 16
=> b = √16
=> b = 4m
Therefore,
the breadth (b) is 4 m.
and
length (l) = \frac{3b}{2}
2
3b
= \frac{3×4}{2}
2
3×4
= \frac{12}{2}
2
12
= \bf{6m}6m
Now,
Area of four walls = \frac{1320}{5.50}
5.50
1320
[ as the cost of painting the walls at the rate of ₹ 5.50 per m² is ₹ 1320 ]
=> Area of four walls = 1320 ÷ \frac{550}{100}
100
550
=> 2(length+breadth) × height = 1320 × \frac{100}{550}
550
100
=> 2(6 + 4) × height = 240
=> 2 × 10 × height = 240
=> 20 × height = 240
=> height = \frac{240}{20}
20
240
=> height = 12 m
Therefore,
the height of the room is 12m.
Hence,
the dimensions of the room are
\bf{length (l)}length(l) = 6m
\bf{breadth (b)}breadth(b) = 4m
\bf{height (h) }height(h) = 12m
Answer:
dimension of room are
lenght=6m
breadth=4m
hieght=12m
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