The perimeter of the floor of a room is 500m. Its length is 10m more than thrice its breadth. Calculate the length and the breadt

2 thoughts on “The perimeter of the floor of a room is 500m. Its length is 10m more than thrice its breadth. Calculate the length and the breadt”

1. Answer:

   Step-by-step explanation:

   The sum of consecutive multiple of 6 is 186. Find its two multiples

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2. Answer :–

   • The length of the room is 190 m.
   • The breadth of the room is 60 m.

   To find :–

   • The length and breadth of the room.

   Solution :–

   • The perimeter of a floor is given to us. We have to find it’s length and breadth. Let’s use the information given to us for forming an equation and solve it to get our answer!

   Let :–

   • The breadth of the floor be “x” m.

   It has been given that :–

   • The length of the floor is 10 m more than thrice it’s breadth.

   Therefore,

   • The length of the floor will be “3x + 10” m.

   Now, we know that :–

   [tex] \underline{ \boxed{\sf Perimeter \: of \: a \: rectangle = 2 \: (L + B)}}[/tex]

   Where,

   • L = Length.
   • B = Breadth.

   Here,

   • Length = “3x + 10” m.
   • Breadth = “x” m.
   • Perimeter = 500 m.

   Substituting the given values in this formula,

   [tex] \longmapsto\rm500 = 2 \: (3x + 10 + x)[/tex]

   [tex] \longmapsto\rm500 = 2 \: (4x + 10)[/tex]

   [tex] \longmapsto\rm500 = 8x + 20[/tex]

   [tex] \longmapsto\rm500 – 20 = 8x[/tex]

   [tex] \longmapsto\rm480 = 8x[/tex]

   [tex] \longmapsto\rm\dfrac{480}{8} = x[/tex]

   [tex] \longmapsto\overline{ \boxed{ \rm60 \: m = x}}[/tex]

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   Therefore, the dimensions of the room are as follows :–

   [tex] \sf Length = 3x + 10 = 3 \times 60 + 10 = 190 \: m.[/tex]

   [tex] \sf Breadth = x = 60 \: m.[/tex]

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