Garden Area

Let:

  x = width

  2x = length (because it is twice as long as the width)

Since the formula for the perimeter of a rectangle is 2(length + width), we use it to find the length and width since the perimeter is already given.

2(2x + x) = 300

2(3x) = 300

6x = 300

x = 50

2x = 100

By substituting the value of x with the ones at the top, we will know that the width is 50 and the length is 100 since 2(50) is 100.

The question asks for the area of the garden and since we now have the width and length of the garden, we may now get the garden's area.

Formula for the area of a rectangle:

Area of rectangle = (Length)(Width)

Area of rectangle = (100)(50)

Area of rectangle = 5000

or you could also do it like this:

Area of rectangle = x(2x)

since ,as seen at the top, x is the width and 2x is the length

Area of rectangle = 2x^2

And after this, just substitute the value of x, which is 50, to the expression

Area of rectangle = 2(50)^2

Area of rectangle = 2(2500)

Area of rectangle = 5000

So the area of the rectangular garden is 5000

Let $P = 300$ be the perimeter.

Let $W$ be the width.

Let $L$ be the length.

Let $A$ be the area.

Given $\frac{P}{2} = W+L$ , $A = W \times L$ and $L = 2W$ ...

$\implies W+L=150$

$\implies L = 150-W=2W$

$\implies 3W = 150$

$\implies W = 50\ \implies L = 100$

$\implies A = 50 \times 100 = \boxed{5000}$