A cuboidal room is 1 and 1/2 as long again as it is broad.
The cost of carpeting the room at the rate of Rs.5 per m sq is Rs.480 and the cost of papering the walls with coloured paper at the rate of Rs.3 per m sq is Rs.360. Find the dimensions of the room .
taking d floor of d room
area=l*b
l=1.5x, b=x
A=1.5x*x=1.5xsquare.......eq 1
4rm d price
1sq meter will cost rs.5
dere4 x square meter will cost rs.480
(480*1)/5=96square meters
area=96.......eq 2
96=1.5x^2mspuare
x^2m=64; x=8
lenght =1.5*8=12; breadth =8
4 d height==> rs.3........1sq meter
den rs.360.........xsq meter
x=120square meter
let area= height*breadth
120=h*8
h=15m
dimension=12m by 8m by 15m
To find the dimensions of the room, we can use the given information about the cost of carpeting and papering.
Let's assume the breadth of the room is "x" meters.
According to the given information, the length of the room is 1 and 1/2 times the breadth. So the length of the room would be (1 + 1/2) * x = (3/2) * x = (3x/2) meters.
To calculate the area of the room, we can use the formula: Area = Length * Breadth.
The area for carpeting is given as 480 Rs., and the rate of carpeting per square meter is 5 Rs. Therefore, the area for carpeting can be calculated as follows:
(3x/2) * x = 480 / 5
(3x/2) * x = 96
Similarly, the area for papering is given as 360 Rs., and the rate of papering per square meter is 3 Rs. Therefore, the area for papering can be calculated as follows:
2 * (h * l + b * l) = 360 / 3
2 * ((3x/2) * x + x * x) = 120
Now, we have two equations:
(3x/2) * x = 96
2 * ((3x/2) * x + x * x) = 120
We can solve these equations simultaneously to find the value of x (breadth), and then calculate the length and height of the room.
I'll simplify the equations and solve them step by step:
Equation 1: (3x/2) * x = 96
Multiplying through by 2 to eliminate the fraction:
3x * x = 192
3x^2 = 192
Equation 2: 2 * ((3x/2) * x + x * x) = 120
Simplifying the equation:
2 * (3x * x/2 + x^2) = 120
3x^2 + 2x^2 = 120
5x^2 = 120
Now, we can solve these equations:
3x^2 = 192
5x^2 = 120
Dividing both equations by their respective coefficients:
x^2 = 192/3
x^2 = 64
Taking the square root of both sides to find the value of x:
x = sqrt(64)
x = 8
So, the breadth of the room is 8 meters.
Now, we can calculate the length of the room:
Length = (3/2) * x
Length = (3/2) * 8
Length = 12 meters
Therefore, the dimensions of the room are: Breadth = 8 meters, Length = 12 meters.