Question

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?

Answer 1

Answer:

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

Answer 2

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

• Let the length of the rectangular garden be L.

• Let the width of the rectangular garden be W.

Given the following data:

• Perimeter = 32 + L feet.

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

The length of the garden is twice its​ width:

$L=2W$ = $W=\frac{L}{2}$

The formula for perimeter of a rectangle.

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

$P=2(L+W)$

Where:

• P is the perimeter of a rectangle.

• L is the length of a rectangle.

• W is the width of a rectangle.

Substituting the parameters into the formula, we have;

$32+L=2(L+\frac{L}{2})\\\\32+L=2L+L\\\\32+L=3L\\\\3L-L=32\\\\2L=32\\\\L=\frac{32}{2}$

Length, L = 16 feet.

For the width:

$W=\frac{L}{2}\\\\W=\frac{16}{2}$

Width, W = 8 feet.

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

$Area = LW\\\\Area = 16 \times 8$

Area = 128 square feet.

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