Trevor and his friends are making a four-square court that will be $10$ feet long and $10$ feet wide. To protect spectators from the action, they will include a safety zone around the outside of the court that will be the same width around each edge. $\newline$ The total area of the court and safety zone together in square feet can be modeled by the expression $(10 + 2x)(10 + 2x)$ , where $x$ is the width of the safety zone in feet. This expression can also be written in the form $4x^2 + 40x + 100$ . $\newline$ What does the quantity $4x^2 + 40x$ represent in the expression? $\newline$ (A)the perimeter around the outside of the safety zone in feet $\newline$ (B)the area of the court in square feet $\newline$ (C)the length of the court and safety zone together in feet $\newline$ (D)the area of the safety zone in square feet

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Q. Trevor and his friends are making a four-square court that will be

10

feet long and

10

feet wide. To protect spectators from the action, they will include a safety zone around the outside of the court that will be the same width around each edge.

\newline

The total area of the court and safety zone together in square feet can be modeled by the expression

(10 + 2x)(10 + 2x)

, where

x

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

4x^2 + 40x + 100

\newline

What does the quantity

4x^2 + 40x

represent in the expression?

\newline

(A)the perimeter around the outside of the safety zone in feet

\newline

(B)the area of the court in square feet

\newline

(C)the length of the court and safety zone together in feet

\newline

(D)the area of the safety zone in square feet

Total Area Expression: The expression for the total area is $(10 + 2x)(10 + 2x)$ , which expands to $4x^2 + 40x + 100$ .
Court Area: The term $100$ represents the area of the court itself, which is $10$ feet by $10$ feet.
Corner Area: The term $4x^2$ represents the area of the four corners of the safety zone, each being $x$ by $x$ feet.
Side Area: The term $40x$ represents the area of the four sides of the safety zone, two being $10x$ feet and two being $x(10 + 2x)$ feet, but since we're only looking for the linear part, it's just $10x$ for each of the four sides.
Total Safety Zone Area: So, $4x^2 + 40x$ represents the total area of the safety zone around the court.