Question

A homeowner uses four wooden beams to build the perimeter of a rectangular deck. Each wooden beam has an equal length of x feet. He uses two beams for two sides of the deck, and he cuts off 4 feet from each of the other two beams for the remaining two sides of the 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?



(1 point)
Responses

A(x)=2x−4

A(x)=4x^2−16x

A(x)=x^2−4x

A(x)=x^2−4

Answer 1

To find the function \( A(x) \) that represents the total area of the rectangular deck in square feet, let's break down the problem.

1. The length of the two sides where beams are not cut will be \( x \) feet each.
2. The length of the other two sides (after cutting off 4 feet from each beam) will be \( x - 4 \) feet each.

The area \( A \) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]
In this case, the length is \( x \) and the width is \( x - 4 \).

Substituting these values in, we have:
\[
A(x) = x(x - 4)
\]

Now, simplify this expression:
\[
A(x) = x^2 - 4x
\]

Thus, the function that represents the total area of the deck, in square feet, is:
\[
\boxed{A(x) = x^2 - 4x}
\]