Question

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

Answer 1

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.

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Solution :

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

We know that,

`\qquad{ \sf{ \pmb{2(Length + Width ) = Perimeter_((rectangle))}}}`

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Substituting the values in the formula :

`{ \dashrightarrow\qquad{ \sf{2(x + x - 8 ) = 50}}}`

`{ \dashrightarrow\qquad{ \sf{2(2x- 8 ) = 50}}}`

`{ \dashrightarrow\qquad{ \sf{4x- 16 = 50}}}`

`{ \dashrightarrow\qquad{ \sf{4x = 50 + 16}}}`

`{ \dashrightarrow\qquad{ \sf{x = (66)/(4) }}}`

`{ \dashrightarrow\qquad{ \bf{x = 16.5}}}`

Therefore,

• The Length of the garden is 16.5 ft .

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`{ \dashrightarrow\qquad{ \sf{Width_((Garden)) = x - 8}}}`

`{ \dashrightarrow\qquad{ \sf{Width_((Garden)) = 16.5 - 8}}}`

`{ \dashrightarrow\qquad{ \bf{Width_((Garden)) = 8.5}}}`

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Therefore,

• The Width of the garden is 8.5 ft .

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Hence,

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

Answer 2

`\bold{\huge{\underline{ Solution }}}`

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

`\bold{ = 50\: ft}`

We know that,

Perimeter of the rectangle

`\sf{ = 2( Length + Breath) }`

• 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

`\sf{ Perimeter\:of\:rectangle = 2( x + 8 + x) }`

`\sf{ 50 = 2( x + 8 + x) }`

`\sf{ 50 = 2( 2x + 8)}`

`\sf{ 50 = 4x + 16}`

`\sf{ 50 - 16 = 4x }`

`\sf{ 34 = 4x }`

`\sf{ x = }{\sf{(34)/(4)}}`

`\sf{ x = 8.5 }`

Thus, The breath of the garden is 8.5 ft

Therefore,

The length of the garden

`\sf{ = x + 8}`

`\sf{ = 8.5 + 8}`

`\sf{ = 16.5\: ft }`

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