By what percentage will increased the total area of the 4 walls of the room?

Question

The length, breadth and height of a room are in the ratio 11 : 5 : 7.
If the breadth is doubled, length is increased by 4 times while the height is halved.
By what percentage will increased the total area of the 4 walls of the room?

Answer 1

68.75% increase

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Length- L = 11x
Breadth- B= 5x
Height- H = 7x
Area of four walls- A= LH*2+BH*2=2H(L+B)=2*7x*(11x+5x)=224*x^2
New dimensions:
Ln=4L
Bn=2B
Hn=1/2H
New area- An=2Hn(Ln+Bn)=2H*1/2*(4L+2B)=7x*(44x+10x)=378*x^2
The difference = 378x^2-224x^2=154x^2
% = 100*154/224=68.75% increase

Answer 2

Room 1, length = 11, breadth = 5, height = 7
Room2 length = 44, breadth = 10 , height = 3,5
Let us calculate the total area for the two rooms,
Room 1
(7x11x2) + ( 7 x5x2) = 224
Room 2
( 10x3,5x2) + (44x3,5x2) = 378
Then the percentage is calculated as follows:
(378 - 224 ) / 224 = 0,6875 or 68,75 %