Connect with knowledgeable individuals and find the best answers at IDNLearn.com. Find the solutions you need quickly and accurately with help from our knowledgeable community.
Sagot :
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

We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.