Area of the four walls of a room is 108m2. If the height and length of the room are in the ratio of 2 : 5 and the height and breadth in the ratio 4 : 5, then the area, in m2, of the floor of the room is(1) 72(2) 54(3) 45(4) 24

Answer: (3)

Let length of the room = l

Highty of the room = h

Breadth of the room = b

Given

h : l = 2 : 5

h : b = 4 : 5

∴ h : l : b = 4 : 10 : 5

Let us consider

h = 4x

l = 10x

b = 5x

Area of the four walls = 2h(l+b) = 108 m²

Area of the four walls = 2 ✕ 4x (10x + 5x)

Area of the four walls = 2 ✕ 60 x² = 108

x² = 108/120

The area of the floor = l ✕ b

The area of the floor = 10x ✕ 5x

The area of the floor = 50x²

The area of the floor = 50 ✕ (108/120)

The area of the floor = 45m²