Answer:

The answer is -

1. Dimension = 3x = 3 X 4(x = 4) = 12 m
2. Dimension = 2x = 2 X 4(x = 4) = 8 m
3. Dimension = 1x = 1 X 4(x = 4) = 4 m

Step-by-step explanation:

To find the dimensions of the room

The dimensions are in the RATIO 3:2:1 and its total surface area is 352 m^2(given)

Step 1 = First LET the dimensions be 3x[l], 2x[B] and x[h](or 1x) respectively

As we know that whenever there are three different dimensions of a room it is considered a cuboid

And we know that total surface area of a cuboid is

Where l = length, b = breadth, h = height

2(lb + bh + lh)

We know that l = 3x, b = 2x and h = x

= 2[(3x)(2x) + (2x)(x) + (3x)(x)]

= 2[6x^2 + 2x^2 + 3x^2]

= 12x^2 + 4x^2 + 6x^2(L.H.S)

Step 2 = Equate the L.H.S[12x^2 + 4x^2 + 6x^2] with R.H.S[352 m^2]

That is,

L.H.S = R.H.S

12x^2 + 4x^2 + 6x^2 = 352

Add the like terms

22x^2 = 352

x^2 = 352/22

      = 16

x = 4

The dimensions are as follows-

1. Dimension = 3x = 3 X 4(x = 4) = 12 m
2. Dimension = 2x = 2 X 4(x = 4) = 8 m
3. Dimension = 1x = 1 X 4(x = 4) = 4 m