Question

The Garden Task

Answer 1

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 = $(side length)^2$

Given:

Perimeter of square (P) = $(14x - 32) ft$

Side length (s) = $(x + 2) ft$

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

$(14x - 32) = 4(x + 2)$

• Solve for x

$14x - 32 = 4x + 8\\\\14x - 4x = 32 + 8\\\\10x = 40\\\\x = 4$

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

• Perimeter of the fence = $(14x - 32) ft$

• Plug in the value of x

Perimeter of the fence = $14(4) - 32 = 24 ft$

Find the area of the garden:

• Area of the garden = $(side length)^2$

Area = $(x + 2)^2$

• Plug in the value of x

Area = $(4 + 2)^2 = 6^2 = 36 ft^2$

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

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