Question

Area of four walls of a room is $108m^2$ . If height and length of room are in the ratio 2: 5 and height and breadth are in the ratio 4: 5. The area of the floor of the room is

• A. $44m^2$
• B. $47m^2$
• C. $45m^2$
• D. $46m^2$

Answer 1

The correct option is C $45m^2$

Given,
length(l) : height(h) = 5 : 2 &
height(h) : breadth(b) = 4 : 5.
So, l : h : b = 10 : 4 : 5.
Let length = 10x, breadth = 5x and height = 4x.
Given, area of four walls of a room = 108 m${}^2$
$\Rightarrow 2(l+b)h=108$
$\Rightarrow (l+b)h=54$
$\Rightarrow (10x+5x)4x=54$
$\Rightarrow 60x^2=54$
$\Rightarrow x^2=\frac{54}{60}$

$\text{Area of floor of the room}=l\times b=10x\times 5x=50x^2=50\times \frac{54}{60}=45m^2$