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.

# The cost of flooring a room at * 25 per square metre

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[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 BlessedAnswer:Dimensions of the room :-

★ Length of the room =

15 m★ Breadth of the room =

20 mGiven:Tofind:ConceptUsed:→ Formula of Area of rectangle :-

Area of rectangle = l × bwhere,

To find the dimensions of the room :-

Let’s do it. →⠀⠀⠀━━━━━━━━━━━━━━━━━━━

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,

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 = 3Substitute the value of x in the dimensions of the room which we’ve let.

⠀⠀━━━━━━━━━━━━━━━━━━━

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.⠀━━━━━━━━━━━━━━━

KnowMorE: