Question

The area of four walls of a room is 108 m2. If the height and length of the room are in the ratio of 2 : 5 respectively and the height and breadth are in the ratio 4 : 5 respectively, then the area of the floor of the room is?? PLsssss reply fast I will mark brianlist

Answer 1

$\bf{\underline{\underline{Question:-}}}$

The area of four walls of a room is 108 m². If the height and length of the room are in the ratio of 2 : 5 respectively and the height and breadth are in the ratio 4 : 5 respectively, then the area of the floor of the room is ?

$\bf{\underline{\underline{Given:-}}}$

• Area of four wall is 108 m²
• Height and length of room are in ratio 2 : 5 respectively and the height and breadth are in ratio 4 : 5

$\bf{\underline{\underline{To\:Find:-}}}$

• Area of the floor of the room is ?

$\bf{\underline{\underline{Solution:-}}}$

Let,

• Length = L
• Breadth = B
• Height = H

:→ Area of Four walls = 2h ( L + B ) = 108 m²

• height : Length = 2 : 5 ( Given )
• height : Breadth = 4 : 5 ( Given )

Therefore

• height : Length : breadth = 4 : 10 : 5

Now,

:→ Height = 4x

:→ Lenght = 10x

:→ Breadth = 5x

So

• Area of 4walls = 2h ( l + b ) = 108

:→$\sf 2 × 4x ( 10x + 5x ) = 108$

:→$\sf 2 × 4x ( 15x ) = 108$

:→ $\sf 120x^2 = 108$

:→ $\sf x^2 = \dfrac{108}{120}$

$\bf{\underline{\underline{Then:-}}}$

• Area of the floor is Length × Breadth × $\bf \dfrac{108}{120}$

:→ Area of the floor is 10x × 5x ×$\bf \dfrac{108}{120}$

:→ Area of the floor is 50x × $\bf \dfrac{108}{120}$

:→ Area of the floor is 5400 ÷ 120

:→ Area of the floor is 45m²

$\bf{\underline{\underline{Hence:-}}}$

• The Area of floor is 45m²

Answer 2

Given :–

• Area of four walls of a room = 108m².
• Height and length of the room are in the ratio = 2:5.
• The height and breadth of the room are in ratio = 4:5.

To Find :–

• Area of the floor of a room.

Solution :–

Let,

• The length = l
• The breadth = b
• The height = h

We know that,

Area of four walls of a room = 2h(l + b)

So,

Given that,

2h(l + b) = 108m²

• h:l = 2:5

• h:b = 4:10

Let us consider,

• h:l:b = 4:10:5

• h = 4x, l = 10x, b = 5x

Now, put the values of h, l, b in the formula of area of 4 walls.

So,

⟹ 2(4x)(10x + 5x)

⟹ 2 × 4x(15x)

Now, open the bracket,

⟹ 2 × 60x² = 108

⟹ x² = $\dfrac{108}{2 \times 60}$

⟹ x² = $\dfrac{108}{120}$

Now, we have to find the area of the floor of a room.

Area of the floor = l × b

Here,

• l = 10x
• b = 5x
• x² = $\dfrac{108}{120}$

Now, put all the values in the formula of area of the floor.

⟹ 10x × 5x

⟹ 50x²

⟹ $5\cancel0 \times \dfrac{\cancel{108}}{12\cancel0}$

⟹ $5 \times \dfrac{\cancel{108}}{\cancel{12}}$

⟹ $5 \times \dfrac{\cancel{54}}{\cancel6}$

⟹ $5 \times \dfrac{\cancel{27}}{\cancel3}$

⟹ 5 × 9

⟹ 45m²

Hence,

The area of the floor of a room is 45m².