Question

A rectangular deck is made up of four wooden beams. The length of the rectangular deck is given by x feet, and the width is 4 feet less than the length, 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?

Answer 1

To find the function \( A(x) \) that represents the total area of the rectangular deck as a function of the length \( x \), we need to determine both the length and the width of the deck.

1. The length of the deck is given as \( x \) feet.
2. The width of the deck is 4 feet less than the length. Therefore, the width can be expressed as:
\[
\text{Width} = x - 4 \text{ feet}
\]

Now, the area \( A \) of a rectangle is calculated using the formula:
\[
A = \text{Length} \times \text{Width}
\]

Substituting the expressions for the length and width into the area formula, we get:
\[
A(x) = x \times (x - 4)
\]

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

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