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mary needs 50 ft of fence to protect her rectangular garden from squirrels. How long and how wide is the garden if the length is 8 ft more than the width

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Starrysoul100

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Given :-

  • Mary needs 50 ft of fence to protect her rectangular garden from squirrel
  • The length of the garden is 8 ft more than the width

To Find :-

  • We have to find the length and breath of the rectangular garden

Let's Begin :-

Mary needs 50ft of fence to protect her rectangular garden from squirrel

Therefore,

We can conclude that

The perimeter of the rectangular garden

[tex]\bold{ = 50\: ft}[/tex]

We know that,

Perimeter of the rectangle

[tex]\sf{ = 2( Length + Breath) }[/tex]

  • Here, we have
  • Length of the garden that is 8ft more than the width

Let assume the width of the garden be x

According to the question

[tex]\sf{ Perimeter\:of\:rectangle = 2( x + 8 + x) }[/tex]

[tex]\sf{ 50 = 2( x + 8 + x) }[/tex]

[tex]\sf{ 50 = 2( 2x + 8)}[/tex]

[tex]\sf{ 50 = 4x + 16}[/tex]

[tex]\sf{ 50 - 16 = 4x }[/tex]

[tex]\sf{ 34 = 4x }[/tex]

[tex]\sf{ x = }{\sf{\dfrac{34}{4}}}[/tex]

[tex]\sf{ x = 8.5 }[/tex]

Thus, The breath of the garden is 8.5 ft

Therefore,

The length of the garden

[tex]\sf{ = x + 8}[/tex]

[tex]\sf{ = 8.5 + 8}[/tex]

[tex]\sf{ = 16.5\: ft }[/tex]

Hence, The length and breath of the rectangle are 8.5ft and 16.5ft .

Given :

  • Mary needs 50 ft of fence to protect her rectangular garden from squirrels.

  • The length is 8 ft more than the width of the garden.

⠀

To Find :

  • The dimensions of the garden.

⠀

Solution :

  • Let us assume the length of the garden as x ft and therefore, the width will become (x - 8) ft.

We know that,

[tex]\qquad{ \sf{ \pmb{2(Length + Width ) = Perimeter_{(rectangle)}}}}[/tex]

⠀

Substituting the values in the formula :

[tex]{ \dashrightarrow\qquad{ \sf{2(x + x - 8 ) = 50}}}[/tex]

[tex]{ \dashrightarrow\qquad{ \sf{2(2x- 8 ) = 50}}}[/tex]

[tex]{ \dashrightarrow\qquad{ \sf{4x- 16 = 50}}}[/tex]

[tex]{ \dashrightarrow\qquad{ \sf{4x = 50 + 16}}}[/tex]

[tex]{ \dashrightarrow\qquad{ \sf{x = \dfrac{66}{4} }}}[/tex]

[tex]{ \dashrightarrow\qquad{ \bf{x = 16.5}}}[/tex]

Therefore,

  • The Length of the garden is 16.5 ft .

⠀

[tex]{ \dashrightarrow\qquad{ \sf{Width_{(Garden)} = x - 8}}}[/tex]

[tex]{ \dashrightarrow\qquad{ \sf{Width_{(Garden)} = 16.5 - 8}}}[/tex]

[tex]{ \dashrightarrow\qquad{ \bf{Width_{(Garden)} = 8.5}}}[/tex]

⠀

Therefore,

  • The Width of the garden is 8.5 ft .

⠀

Hence,

  • The dimensions of the rectangular garden is 16.5 ft and 8.5 ft.
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