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: If the breadth and height are halved, while the length is doubled, then the total area of the 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) = 2(x)(3x + 2x) = 2(x)(5x) = 10x² 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

\text { Area }_{\text {new }} = 2(x/2)(6x + x) = 2 × (x/2) × (7x) = 7x²

\text { Area }_{\text {original }} = 10x²

The percentage increase = \left(\text { Are } a_{\text {new }} \text { - Area }_{\text {original }}\right) / \text { Area }_{\text {original }}

The percentage difference in the area of four walls = [ (7x² - 10x²) / 10x² ] × 100 = [ - 3x² / 10x² ] × 100 = [ -3/10 ]  × 100 = - 30 %

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

Thus, if the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will decrease by 30%.