Length, breadth and height of a room are in the ratio 9:7:5. If breadth and length are doubled while height is halved...

Question

The length, breadth and height of a room are in the ratio 9:7:5. If the breadth and length are doubled while the height is halved. Then what would be the impact on the total area of the 4 walls of the room (in terms of percentage)?

Answer 1

L:B:H = 9:7:5
let x be such that 9x = length, 7x = Breadth & 5x = Height.
After changes in dimension
L1:B1:H1 = 9*2*x:7*2*x:5*0.5*x = 18x:14x:2.5x

Now (((L1*H1+B1*H1) - (L*H + B*H)) / (L*H + B*H))
= (((18x*2.5x + 14x*2.5x) - (9x*5x + 7x*5x))/(9x*5x + 7x*5x)
= (80x^2 - 80x^2) / 80x^2 = 0
ie., the area of the walls remain the same.

Answer 2

To begin with, you have two walls that are 9x5, or 90 units. Then, you have two 7x5 walls for a total of 70 units, making the total area 160 units. Then, you have two walls that are 18 x 2.5 units, for 90 units. Then, two more walls, at 14x2.5 each, or 70 units. Once again, we have a grand total of 160 units. So, there is no change in the total areas......