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 d

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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

  2. 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

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