Question

the length and the breadth of a hall are in the ratio 4:3 and it's height is 5.5 meter.The cost of decorating it's walls (including doors and windows) at rupee 6.60 per square meter is rupee 5082. Find the length and breadth of the room.​

Answer 1

$\large\bold{\underline{\underline{Answer:}}}$

Length = 40m

Breadth = 30m

$\bold{\underline{Given\:that:-}}$

• Length of the hall in the ratio are 4:3.

• Height of the hall = 5.5 meter.

• Cost of decorating walls (including doors & windows) at rupees 6.60 per sq. meter is rupees 5082.

$\bold{\underline{To\:find:-}}$

• Length of the room.

• Breadth of the room.

$\huge\bold{\underline{\underline{Solution:}}}$

_________________________

▪Let the length be 4x

▪ Let the Breadth be 3x

Now, Area of walls × rate = Cost of painting

2 (Length + Breadth) × height × 6.60 = 5082

2 (4x + 3x) × 5.5 × 6.60 = 5082

$\leadsto$ 7x = $\frac{5082}{5.5\times2.6\times2}$

$\leadsto$ 7x = 10

$\leadsto$ x = 10

Therefore,

Length = 4x = 4 × 10 = 40m

Breadth = 3x = 3 × 10 = 30m

Hence, Solved!

Answer 2

The ratio of length and breadth of the hall is $\sf{4:3}$

Length of the room : 4x m

Breadth of the room : 3x m

Also, height of the hall is 5.5 m.

From the given dimensions we can be pretty much sure that the hall is cuboidal shaped.

The walls of hall is to be decorated and the cost of decorating is ₹ 6.60 per square meter.

And the cost of decorating the entire hall's wall costs ₹ 5082.

It is known that, area equals the total cost over the rate per square metre.

Formula form :

$\sf{Area\:=\dfrac{Total\:cost}{Rate\:per\: square\: metre}}$

Since mentioned earlier the supposed shape is cuboid and we are decorating just the walls, we are going to use the formula for lateral surface of cuboid.

=> $\sf{2(l+b)h=\:\dfrac{5082}{6.60}}$

=> $\sf{2(l+b)h=\:\dfrac{5082\:\times\:100}{6.60\:\times\:100}}$

=> $\sf{2(4x+3x) \times\:5.5=\dfrac{508200}{660}}$

=> $\sf{2(7x)\: \times\:5.5=770}$

=> $\sf{14x\:\times\:5.5=770}$

=> $\sf{77x=770}$

=> $\sf{x=\dfrac{770}{77}}$

=> $\sf{x=10}$

Since,x = 10 and the length and breadth are in the ratio of 4:3, therefore length of the room will be 4 times the value of x and breadth of the room will be 3 times the value of x.

$\bold{\purple{Length\: of\: the \:room\: = \:4 \times\: 10 = 40 m}}$

$\bold{\purple{Breadth\: of\: the \:room\: = \:3 \times\: 10 = 30 m}}$