Question 39

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

Solution

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Let length be 3x, breadth be 2x, and height be x
Now we know that the area of four walls = 2h(l+b) = 2x(5x) = 10$$x^2$$
Now new length = 6x , new height = 0.5x and new breadth = x
So the area of four walls will now be: 2(0.5x)(7x)= 7$$x^2$$
Now therefore percentage change in area : $$\frac{7x^2-10x^2}{10x^2}\times\ 100\ =\ -30\%$$

Hence, the area decreases by 30%.

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