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The Garden Task
You want to fence the square
garden shown below. The garden
has a perimeter of 14x - 32 and one
of the sides is (x + 2) ft. How much
fencing do you need? What is the
area of the garden? If the garden
doubled its size, what would the
perimeter & area be of the new
garden?
x+2

Sagot :

akposevictor

If the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

  • the perimeter = 24 ft
  • the area = 36 sq. ft
  • if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
  • if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Recall:

  • A square has equal side lengths
  • Perimeter of a square = 4(side length)
  • Area of a square = [tex](side $ length)^2[/tex]

Given:

Perimeter of square (P) = [tex](14x - 32) $ ft[/tex]

Side length (s) = [tex](x + 2) $ ft[/tex]

First, let's find the value of x by creating an equation using the perimeter formula:

  • Perimeter of a square = 4(side length)

  • Plug in the values

[tex](14x - 32) = 4(x + 2)[/tex]

  • Solve for x

[tex]14x - 32 = 4x + 8\\\\14x - 4x = 32 + 8\\\\10x = 40\\\\x = 4[/tex]

Find how much fencing would be needed (Perimeter of the fence):

  • Perimeter of the fence = [tex](14x - 32) $ ft[/tex]

  • Plug in the value of x

Perimeter of the fence = [tex]14(4) - 32 = 24 $ ft[/tex]

Find the area of the garden:

  • Area of the garden = [tex](side $ length)^2[/tex]

Area = [tex](x + 2)^2[/tex]

  • Plug in the value of x

Area = [tex](4 + 2)^2 = 6^2 = 36 $ ft^2[/tex]

Find the perimeter if the garden size is doubled:

  • Perimeter of the new garden = 2 x 24 = 48 ft

Find the area if the garden size is doubled:

  • Perimeter of the new garden = 2 x 36 = 72 sq. ft

In summary, if the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

  • the perimeter = 24 ft
  • the area = 36 sq. ft
  • if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
  • if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Learn more here:

https://brainly.com/question/13511952

View image akposevictor
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