# The length, breadth, and height of a room are in the ratio 3:2:1. If the breadth and height are halved, while the length is doubled, then the total area of the four walls of the room will:

# (1) Remain the same (2) Decrease by 30% (3) Decrease by 15% (4) Decrease by 18.75%

The area of the room is calculated by the concept of the lateral surface area of the cuboid.

## Answer: Option (2), the total area of four walls of the room will decrease by 30%.

Let's understand the surface area of the cuboid in detail.

**Explanation:**

Let the length, breadth, and height of the cuboid as 3x, 2x, and x respectively.

Then the area of four walls is given by 2(bh + lh) = 2h(l + b)

The area of four walls: 2(x)(3x + 2x) = 2(x)(5x) = 10x^{2 }sq.m

Given that,

- length is doubled: (3x) × 2 = 6x
- breadth is halved: 2x / 2 = x
- height is halved: x / 2 = x/2

Now, the new area of four walls = 2h(l + b)

Area_{new} = 2(x/2)(6x + x) = 2 × (x/2) × (7x) = 7x^{2}

Area_{original }= 10x^{2}

The percentage increase = (Area_{new} - Area_{original}) / Area_{original}

The percentage difference in the area of four walls = [ (7x^{2} - 10x^{2}) / 10x^{2 }] × 100 = [ - 3x^{2} / 10x^{2 }] × 100 = [ -3/10 ] × 100 = - 30 %

The percentage difference in the area of four walls is - 30% (Negative sign shows decrease in area)