Question

A Home owner uses 4 wooden things to build the preameter of a rectangular deck.Each wooden beam has an equal length of x feet.He uses two beams 42 sides of the deck and he cuts Off 4 feet from each of the other 2 beams for the remaining 2 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.
A(x) = x^2 = 4x
A(x) =4x ^2 - 16x
A(x) = 2x -4
A(x) = x^2 -4

Answer 1

To determine the function \( A(x) \) that represents the total area of the rectangular deck in square feet based on the given information, let's break down the information step by step:

1. **Beams Description**:
- Two beams have a length of \( x \) feet (for the longer sides of the rectangle).
- The other two beams are cut down by 4 feet, resulting in a length of \( x - 4 \) feet (for the shorter sides of the rectangle).

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

3. **Function for Area**:
Therefore, the area \( A(x) \) can be expressed as:
\[
A(x) = x \cdot (x - 4)
\]
Expanding this equation:
\[
A(x) = x^2 - 4x
\]

The resulting function that represents the total area of the deck in square feet is:
\[
A(x) = x^2 - 4x
\]

Hence, the correct choice from the provided options is:
**A(x) = x^2 - 4x**.