Venture Properties is looking to design a new food-truck park. The dimensions of the rectangular park will be $110$ feet by $80$ feet. The parking lot will be along two sides of the park, and it will be the same width on both sides. $\newline$ The total area of the park and parking lot together in square feet can be modeled by the expression $(x + 80)(x + 110)$ , where $x$ is the width of the parking lot in feet. $\newline$ What does the quantity $x + 110$ represent in the expression? $\newline$ (A)the length of the park and parking lot together in feet $\newline$ (B)the perimeter around the outside of the park and parking lot in feet $\newline$ (C)the area of the parking lot in square feet $\newline$ (D)the total area of the park and parking lot together in square feet

Full solution

Q. Venture Properties is looking to design a new food-truck park. The dimensions of the rectangular park will be

110

feet by

80

feet. The parking lot will be along two sides of the park, and it will be the same width on both sides.

\newline

The total area of the park and parking lot together in square feet can be modeled by the expression

(x + 80)(x + 110)

, where

x

is the width of the parking lot in feet.

\newline

What does the quantity

x + 110

represent in the expression?

\newline

(A)the length of the park and parking lot together in feet

\newline

(B)the perimeter around the outside of the park and parking lot in feet

\newline

(C)the area of the parking lot in square feet

\newline

(D)the total area of the park and parking lot together in square feet

Total Area Expression: The expression for the total area is x + 80)(x + 110)\. To understand what \$x + 110)\ represents, let's look at the dimensions given for the park: \${110} feet by ${80}$ feet.
Width Calculation: The width of the parking lot is $x$ feet on both sides. So, the total width of the park including the parking lot on one side is $80 + x$ feet.
Length Calculation: Similarly, the length of the park is $110$ feet, and the parking lot will add $x$ feet to this length on one side. So, the total length of the park including the parking lot on one side is $110 + x$ feet.
Total Length Representation: Therefore, $x + 110$ represents the total length of the park and parking lot together in feet.