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

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

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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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