The length of a room is 50 per cent more than its breadth.The cost of carpeting the room at the rate of Rs 38.50m2 is Rs 924 and tne cost of papering the wall @ rupees 3.30 m^2 is rupees 214.50. if the room has one door of dimensions 1 m * 2 m and two windows eacg of dimensions 1 m and 1.5 m
Answers
Answer:
Let,
the breadth of the room be m.
According to the question,
the length of the room is 50% more than its breadth.
length = + 50% of
length = + ×
length = +
length =
Now,
Area of the floor =
[ as the cost of carpeting the room at the rate of ₹ 38.50 m² is ₹ 924 ]
=> Area of the floor = 924 ÷
=> length × breadth = 924 ×
=> × b = 24
=> \frac{3 {b}^{2} }{2} = 24
=> 3b² = 24 × 2
=> 3b² = 48
=> b² =
=> b² = 16
=> b = √16
=> b = 4m
Therefore,
the breadth (b) is 4 m.
and
length (l) = = = =
Now,
Area of four walls =
[ as the cost of painting the walls at the rate of ₹ 5.50 per m² is ₹ 1320 ]
=> Area of four walls = 1320 ÷
=> 2(length+breadth) × height = 1320 ×
=> 2(6 + 4) × height = 240
=> 2 × 10 × height = 240
=> 20 × height = 240
=> height =
=> height = 12 m
Therefore,
the height of the room is 12m.
Hence,
the dimensions of the room are
= 6m
= 4m
= 12m
Step-by-step explanation:
Question :
The length of a room is 50% more than its breadth. The cost of carpeting the room at the rate of ₹38.50 m² is ₹924 and the cost of papering the walls at ₹3.30 m² is ₹214.50 . If the room has one door of dimensions 1 m × 2 m and two windows each of dimensions 1 m × 1.5 m, find the dimensions of the room.
Given :
The length of a room is 50% more than its breadth.
The cost of carpeting the room at the rate of ₹ 38.50
The cost of papering the walls at ₹ 3.30 m² is ₹ 214.50
One dimension of the room = 1 m × 2 m.
Second dimension of the room = 1 m × 1.5 m.
To Find :
The dimensions of the room = ?
Solution :
Let the breadth of a room be (x)m. Then,
Length = x + 50 % of x
= x + 50/100 × x
= x + x/2
= 2x + x/2
= 3x/2
Area of floor = 924/38.50
=> l × b = 924 × 100/3,850
=> x × 3x/2 = 24
=> 3x²/2 = 24
=> x² = 24 × 2/3
=> x² = 16
=> x = √16
=> x = 4
Hence , breadth = 4m
length = 3 × 4/2
= 6m
Area of four walls = 1,320/5.50
=> 2(l+b) × h = 1,320 × 100/5.50
=> 2(6+4) × h = 240
=> 10h = 240/2
=> 10h = 120
=> h = 120/10
=> h = 12m
Final solution :
Dimensions of room are 6m × 4m × 12m .