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

[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 Reply

Answer : 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 To find : 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. → ⠀⠀⠀━━━━━━━━━━━━━━━━━━━ 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 ⠀⠀━━━━━━━━━━━━━━━━━━━ 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. ⠀━━━━━━━━━━━━━━━ 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 Reply

[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: