Question

10. The length, breadth and height of a rectangular room are in the ratio 3:2 : 4. If the difference
between the cost of colouring it at the rate of 8 and 9.77 per m is * 1472. Find the dimensions
of the room.​

Answer 1

Answer:

Length=15.20m

Breadth=10.80m

Height  =21.60m        

Step-by-step explanation:

Let Length of room=3x

Breadth of room=2x

Height of room=4x

We know that,Surface Area of Cuboid=2Height(Length+Breadth)

If floor and roof  are not coloured,and rest of the wall are colouring including roof

Area to be coloured=2Height(Length+Breadth)

                                                 =$2\times 4x(3x+2x)$

                                                 =$2\times4x(5x)$

                                                 =$40x^2$

Case1: When cost of colouring =Rs.8/m

Total cost of colouring a room=$Cost\ of\ colouring\ per\m\times Area\ of\ Room\ to\ be\ painted$

Total Cost of colouring a room=$8\times 40x^2$

               =$Rs.320x^2$

Case2: When cost of colouring a room =Rs.9.77/m

Total cost of Painting a room=$Cost\ of\ Colouring\ per\ m\times Area\ of\ Room\ to\ be\ colouring$

Total Cost of Colouring a room=$9.77\times 40x^2$

                                                =$Rs. 390x^2$

Now,According to Question,

Difference Between Cost of colouring it at the rate of 8 and 9.77 per m= 1472.

⇒Difference Between Cost of colouring it at the rate of 8 and 9.77 per m=$390x^2-320x^2$

⇒$50x^2=1472$

⇒$x^2=29.22$

⇒x= 5.40

So,$Length=3\times 5.40$

      Length=15.20m

 Breadth=$2\times 5.40$

 Breadth=10.80m

Height=$4\times5.40$

Height  =21.60m        

                   

Answer 2

this is very difficult leave this question