area of the floor of a cuboidal party hall is 80 metre square if the area of the walls of the hall is 135 meter square and 108 meter square what is the height of the hall?
Answers
Answer:
The perimeter of Floor is given as 2(l+b)=250m
The height of walls h=6m
The Lateral surface area is 2h(l+b)=6×2501500m2
Cost of 1m2 is 8
Cost of 1500m2 is 8×150012000Rs.
Given,
The area of the floor of a cuboidal party hall = 80 m^2
The area of the walls of the hall is 135 m^2 and 108 m^2
To find,
The height of the hall.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that the length, breadth, and height of the room are x, y, and z m, respectively.
As per mensuration;
Area of the floor of a room = length × breadth
Area of the walls of a room = length/breadth × height
{Statement-1}
Now, according to the question;
The area of the floor of a cuboidal party hall = 80 m^2
=> length × breadth = 80 m^2
=> x m × y m = 80 m^2
=> xy = 80
{Equation-1}
And, the area of the first wall = 135 m^2
=> length × height = 135 m^2
=> x m × z m = 135 m^2
=> xz = 135
{Equation-2
And, the area of the second wall = 108 m^2
=> breadth × height = 108 m^2
=> y m × z m = 108 m^2
=> yz = 108
{Equation-3}
Now, multiplying equation-1, equation-2, and equation-3, we get;
xy × xz × yz = 80×135×108
=> (xyz)^2 = 4×4×5×5×9×9×6×6 = (4×5×6×9)^2
=> xyz = 1080
=> (xy) × z = 1080
=> 80 × z = 1080
{according to equation-1}
=> z = 1080/80 = 13.5 m
=> height of the hall = 13.5 m
Hence, the height of the hall is equal to 13.5 m.