Question

The diagram shows the floor plan for a rectangular storage facility. All dimensions are given in feet.
L 4x-3
W 2x+5

Which expression represents the area of the storage facility in square feet?

Answer 1

To find the area \( A \) of a rectangular storage facility, we use the formula:

\[
A = L \times W
\]

Where:
- \( L \) is the length of the facility, given as \( L = 4x - 3 \)
- \( W \) is the width of the facility, given as \( W = 2x + 5 \)

Substituting the expressions for length and width into the area formula:

\[
A = (4x - 3)(2x + 5)
\]

Now, we need to expand this expression using the distributive property (also known as the FOIL method for binomials):

1. Multiply the first terms:
\[
4x \cdot 2x = 8x^2
\]

2. Multiply the outer terms:
\[
4x \cdot 5 = 20x
\]

3. Multiply the inner terms:
\[
-3 \cdot 2x = -6x
\]

4. Multiply the last terms:
\[
-3 \cdot 5 = -15
\]

Now, combine these results:

\[
A = 8x^2 + 20x - 6x - 15
\]

Combine the like terms (the \( x \) terms):

\[
A = 8x^2 + (20x - 6x) - 15
\]
\[
A = 8x^2 + 14x - 15
\]

Therefore, the expression that represents the area of the storage facility in square feet is:

\[
\boxed{8x^2 + 14x - 15}
\]