One length of a rectangular garden lies along a patio wall. However, the rest of the garden is enclosed by 32 feet of fencing. If the length of the garden is twice its width, what is the area of the garden?

The area of the rectangular garden is equal to 128 square feet.

Given the following data:

Translating the word problem into an algebraic equation, we have;

The length of the garden is twice its width:

=

Mathematically, the perimeter of a rectangle is given by the formula;

Where:

Substituting the parameters into the formula, we have;

Length, L = 16 feet.

For the width:

Width, W = 8 feet.

Now, we can calculate the area of the rectangular garden:

Area = 128 square feet.

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128 square feet

Step-by-step explanation:

Let the perimeter of the rectangular garden be expressed as 2(L+W)

L = length of the garden

W = width of the garden

If the length of the garden is twice its width then L = 2W; W = L/2

P = 2(L+L/2)

Since the perimeter is L + 32 (One length of a rectangular garden that lies along a patio wall and the rest of the garden is enclosed by 32 feet of fencing.)

Substituting in the formula above:

32+L = 2(L+L/2)

32+L = 2L+L

32 = 2L

L = 16 feet

Since L = 2W

W = L/2 = 16/2

Width = 8 feet

Area of the garden = Length × Width

Area of the garden = 16×8

Area of the garden = 128 square feet

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