Respuesta :

Given :

  • The area of rectangular garden is 27000m² .

  • The ratio of length and breadth is 10 : 3 .

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To Find :

  • The perimeter of the rectangular garden.

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Solution :

Let us assume the length as 10x m and breadth as 3x m .

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We know that,

[tex]{ \longrightarrow{\quad \sf \pmb{ Length \times Breadth = Area_{(rectangle)}}} }[/tex]

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Now, substituting the values in the formula :

[tex]{ \longrightarrow{\quad \sf{ 10x \times 3x = 27000 }}} [/tex]

[tex]{ \longrightarrow{\quad \sf{ 30 {x}^{2} = 27000 }}} [/tex]

[tex]{ \longrightarrow{\quad \sf{ {x}^{2} = \dfrac{27000}{30} }}} [/tex]

[tex]{ \longrightarrow{\quad \sf{ {x}^{2} = 900 }}} [/tex]

[tex]{ \longrightarrow{\quad \sf{ {x}= \sqrt{900} }}} [/tex]

[tex]{ \longrightarrow{\quad \bf{ {x}= 30 }}} [/tex]

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Therefore,

  • Length = 10x m = 10(30) m = 300 m
  • Breadth = 3x m = 3(30) m = 90 m

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Now,

We know that,

[tex]{ \longrightarrow{\quad \sf \pmb{Perimeter_{(rectangle)}=2(Length + Breadth) }} }[/tex]

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Substituting the values in the formula :

[tex]{ \longrightarrow{\quad \sf {Perimeter_{(rectangle)}=2(300 + 90) }} }[/tex]

[tex]{ \longrightarrow{\quad \sf {Perimeter_{(rectangle)}=2(390) }} }[/tex]

[tex]{ \longrightarrow{\quad \bf \pmb {Perimeter_{(rectangle)}=780 }} }[/tex]

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Therefore,

  • The perimeter of the rectangular garden is 780 m .
ajeigbeibraheem

The perimeter of the rectangle whose area is 27000 m² is 780 m.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the determinating of all the sides of the rectangle. In the given question, we have the following parameters:

Given that:

  • The area of the rectangle = 27000 m²
  • The ratio of the length and the breadth is 10: 3

It implies that, if the length is 10x, the breadth is 3x

The area of a rectangle = length × breath

27000 m² = (10x) × (3x)

27000 m² = 30x²

x² = 27000/30

x² = 900

x = √900

x = 30

Now, we can say that:

  • The length  = 10(30) = 300
  • The breath = 3(30) = 90

The perimeter of the rectangle = 2(length + breadth)

The perimeter of the rectangle = 2(300 + 90)

The perimeter of the rectangle = 780 m

Learn more about the perimeter of a rectangle here:

https://brainly.com/question/19819849

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