Mr. Larry, of Larry's Landscaping, is designing a backyard garden for a client. For visual appeal, the client has requested that the length of the garden be equal to twice the width. The client has also asked for the garden to have a rock edging $2$ feet wide around three sides, since the backyard fence will be along the fourth side. $\newline$ The total area of the garden and edging in square feet can be modeled by the expression $(2x + 4)(x + 2)$ , where $x$ is the width of the garden in feet. This expression can also be written in the form $2x^2 + 8x + 8$ . $\newline$ What does the quantity $8x + 8$ represent in the expression? $\newline$ Choices: $\newline$ (A)the length of the garden and edging together in feet $\newline$ (B)the area of the edging in square feet $\newline$ (C)the area of the garden in square feet $\newline$ (D)the perimeter around the outside of the edging in feet

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Q. Mr. Larry, of Larry's Landscaping, is designing a backyard garden for a client. For visual appeal, the client has requested that the length of the garden be equal to twice the width. The client has also asked for the garden to have a rock edging

2

feet wide around three sides, since the backyard fence will be along the fourth side.

\newline

The total area of the garden and edging in square feet can be modeled by the expression

(2x + 4)(x + 2)

, where

x

is the width of the garden in feet. This expression can also be written in the form

2x^2 + 8x + 8

\newline

What does the quantity

8x + 8

represent in the expression?

\newline

Choices:

\newline

(A)the length of the garden and edging together in feet

\newline

(B)the area of the edging in square feet

\newline

(C)the area of the garden in square feet

\newline

(D)the perimeter around the outside of the edging in feet

Total Area Expression: The expression for the total area is $(2x + 4)(x + 2)$ , which expands to $2x^2 + 4x + 4x + 8$ .
Combine Like Terms: Combine like terms in the expanded expression to get $2x^2 + 8x + 8$ .
Area of Garden: The term $2x^2$ represents the area of the garden, since the length is twice the width ( $2x \times x$ ).
Area of Edging: The term $8x + 8$ must then represent the area of the edging, since it's the remaining part of the total area expression after accounting for the garden's area.
Visualize Garden and Edging: To confirm, let's visualize the garden and edging. The garden is $x$ feet wide and $2x$ feet long. The edging is $2$ feet wide around three sides.
Calculate Area of Longer Strips: The area of the edging can be broken down into three parts: two strips of length $2x$ and width $2$ , and one strip of length $x$ and width $2$ .
Calculate Area of Shorter Strip: Calculate the area of the two longer strips: $2$ strips $\times (2x \times 2) = 4x \times 2 = 8x$ .
Calculate Area of Shorter Strip: Calculate the area of the two longer strips: $2$ strips $\times (2x \times 2) = 4x \times 2 = 8x$ .Calculate the area of the shorter strip: $1$ strip $\times (x \times 2) = 2x$ .