Question

sergio is designing a seating area for a park in boston. the seating area is rectangular, and will surround a garden (solid line) as shown below (not drawn to scale):

suppose the length of the garden (blue rectangle) is ( x ), and the width of the garden is two times its length. the area of sergios park in boston (the rectangle enclosing the garden and the seating area) can be expressed as (write an expression in terms of ( x )).

in expanded form, the area is

Explanation:

Step1: Find the dimensions of the outer rectangle

The length of the garden is \(x\) feet. The width of the garden is \(2x\) feet.
The length of the outer rectangle is \((x + 5+5)=(x + 10)\) feet.
The width of the outer rectangle is \((2x+2 + 2)=(2x + 4)\) feet.

Step2: Use the formula for the area of a rectangle

The area formula for a rectangle is \(A=\text{length}\times\text{width}\).
So, \(A=(x + 10)(2x + 4)\)

Step3: Expand the expression

$$
LATEXBLOCK0
$$

Answer:

The area as a product: \((x + 10)(2x + 4)\)
The expanded - form area: \(2x^{2}+24x + 40\)