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Blue-Green Lagoons is a company that designs and installs wading pools. The standard design includes a rectangular pool that is $2$ times as long as it is wide. The wading pool has an $8$-foot-wide patio on all sides.$\newline$The total area of the pool and patio in square feet can be modeled by the expression $(2x + 16)(x + 16)$, where $x$ is the width of the pool in feet. This expression can also be written in the form $2x^2 + 48x + 256$.$\newline$What does the quantity $48x + 256$ represent in the expression?$\newline$Choices:$\newline$(A)the area of the patio in square feet$\newline$(B)the length of the pool and patio together in feet$\newline$(C)the perimeter around the outside of the patio in feet$\newline$(D)the area of the pool in square feet