# The cost of flooring a room at * 25 per square metreis * 4,500. If length and breadth are in the ratio5: 4. Find the d

The cost of flooring a room at * 25 per square metre
is * 4,500. If length and breadth are in the ratio
5: 4. Find the dimensions of the room.​

### 2 thoughts on “The cost of flooring a room at * 25 per square metre<br />is * 4,500. If length and breadth are in the ratio<br />5: 4. Find the d”

1. [tex]\huge{ \underline{\boxed{\red{ \color{red}{\textsf {\textbf{An}{\color{blue}{\textbf {\textsf{sw}}{\color{green}{\textbf{\textsf{er}}}{\color{orange}{\textsf{\textbf{~:-}}}}}}}}}}}}}[/tex]

[tex]\colorbox{green}{Area of the room :-}[/tex]

⠀⠀⠀➠ Area = Total cost of flooring ÷ Rate of flooring

⠀⠀⠀➠ Area = 4500 ÷ 25

⠀⠀⠀➠ Area = 180

Area of the room = 180 m²

Let,

Length of the room = 5x

Breadth of the room = 4x

[tex]\colorbox{green}{Using formula, }[/tex]

Area of rectangle = l × b

⠀⠀⠀➠ 180 = 5x × 4x

⠀⠀⠀➠ 180 = 20x²

⠀⠀⠀➠ 180/20 = x²

⠀⠀⠀➠ 18/2 = x²

⠀⠀⠀➠ 9 = x²

⠀⠀⠀➠ Taking square root on both the sides.

⠀⠀⠀➠ √9 = x

⠀⠀⠀➠ ± 3 Reject – ve = x

⠀⠀⠀➠ 3 = x

[tex]\colorbox{green}{The value of x = 3}[/tex]

Substitute the value of x in the dimensions of the room which we’ve let.

➠Length of the room = 5x = 5 × 3 = 15 m

➠Breadth of the room = 4x = 4 × 3 = 20 m

✰✫✰✫✰✫✰✫✰✫✰✫

♬♫♪

Stay happy N Blessed

Dimensions of the room :-

★ Length of the room = 15 m

★ Breadth of the room = 20 m

### Given :

• Rate of flooring a room = Rs. 25
• Total cost of flooring = Rs. 4,500
• Ratio of length and breadth of the room = 5 : 4

### Tofind :

• Dimensions of the room

### Concept Used :

→ Formula of Area of rectangle :-

• Area of rectangle = l × b

where,

• l = length of the rectangle
• b = breadth of the rectangle

To find the dimensions of the room :-

• Firstly, find the area of the room.
• To find the area :- divide the total cost of flooring the room by the rate of flooring the room. The resultant value will be the area of the room.
• Now, assume the length and breadth of the room as 5x and 4x respectively and by using the formula of area of rectangle. Find the value of x.
• Substitute the value of x in the dimensions of the room that will be the required answer.

Let’s do it. →

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### Solution :

Area of the room :-

⠀⠀⠀⇒ Area = Total cost of flooring ÷ Rate of flooring

⠀⠀⠀⇒ Area = 4500 ÷ 25

⠀⠀⠀⇒ Area = 180

Area of the room = 180 m²

Let,

• Length of the room = 5x
• Breadth of the room = 4x

Using formula,

Area of rectangle = l × b

⠀⠀⠀⇒ 180 = 5x × 4x

⠀⠀⠀⇒ 180 = 20x²

⠀⠀⠀⇒ 180/20 = x²

⠀⠀⠀⇒ 18/2 = x²

⠀⠀⠀⇒ 9 = x²

⠀⠀⠀⇒ Taking square root on both the sides.

⠀⠀⠀⇒ √9 = x

⠀⠀⠀⇒ ± 3 Reject – ve = x

⠀⠀⠀⇒ 3 = x

The value of x = 3

Substitute the value of x in the dimensions of the room which we’ve let.

• Length of the room = 5x = 5 × 3 = 15 m
• Breadth of the room = 4x = 4 × 3 = 20 m

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Verification :

Substitute the value of x in 180 = 5x × 4x

⠀⠀⠀⇒ LHS = 180

Taking RHS,

⠀⠀⠀⇒ 5x × 4x

⠀⠀⠀⇒ (5 × 3) × (4 × 3)

⠀⠀⠀⇒ 15 × 12

⠀⠀⠀⇒ 180

RHS = 180

LHS = RHS

Hence, verified.

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### Know MorE :

• Area of square = side × side
• Perimeter of square = 4 × side
• Diagonal of square = √2a
• Perimeter of reactangle = 2(l + b)
• Diagonal of rectangle = √l² + √b²
• Total surface Area of cuboid = 2(lb + bh + hl)
• Volume of cuboid = length × breadth × height
• Total surface area of cube = 6 × side²
• Volume of cube = side³