Question

question 1 - 21. a homeowner uses this rectangle to build the perimeter of a rectangular deck, as shown by the diagram below. the total area of the deck, in square feet, is a function of the distance x, in feet. what is the function, a(x), that represents the total area of the deck, in square feet? o a(x)=x² - 4 o a(x)=x² - 4x o a(x)=4x² - 16x o a(x)=2x - 4

Explanation:

Step1: Recall area formula for rectangle

The area formula for a rectangle is $A = length\times width$. Here, the length and width of the rectangle - shaped deck are both $x$.

Step2: Calculate the area function

Substitute length = $x$ and width = $x$ into the area formula. So $A(x)=x\times x=x^{2}$.

Answer:

The function $A(x)$ that represents the total area of the deck is $A(x)=x^{2}$. So the correct option is the one with $A(x) = x^{2}$.