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)=x2−4x cap A times x is equal to x squared minus 4 x A(x)=2x−4 cap A times x is equal to 2 x minus 4 A(x)=4x2−16x cap A times x is equal to 4 x squared minus 16 x A(x)=x2−4

Answer 1

To find the function \( A(x) \) that represents the total area of the deck, we need to determine the dimensions of the rectangular deck based on the descriptions provided.

### Dimensions of the Deck:
1. Two sides of the deck each have a length of \( x \) feet (the beams that were not cut).
2. For the other two sides, the homeowner cuts off 4 feet from each of the beams, so these sides will have a length of \( x - 4 \) feet.

### Area of the Deck:
The area \( A \) of a rectangle is given by the formula:
\[
A = \text{Length} \times \text{Width}
\]
In this case, the length of the deck can be considered \( x \) and the width can be \( x - 4 \).

Thus, the area function \( A(x) \) can be expressed as:
\[
A(x) = x \times (x - 4)
\]
### Simplifying the Area Function:
Now, we can simplify this expression:
\[
A(x) = x^2 - 4x
\]

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