Question

The length of a garden plot is 6 meters less than 5 times the width. Which equation describes the relationship between the width `w` of the plot in meters, and the area `A` in square meters?
A. A = 5w^2
B. A = 5w^2 - 6w
C. A = 5w - 6
D. A = 5 (w^2 - 6)

Answer 1

To find the equation that describes the relationship between the width \( w \) of the garden plot and its area \( A \), we need to express the length in terms of the width and then use the formula for area.

1. **Express the length in terms of width:**
The problem states that the length \( l \) is 6 meters less than 5 times the width:
\[
l = 5w - 6
\]

2. **Use the formula for area:**
The area \( A \) of a rectangle (which the garden plot is) is given by:
\[
A = l \cdot w
\]
Substituting the expression for length into the area formula:
\[
A = (5w - 6) \cdot w
\]

3. **Distribute \( w \):**
\[
A = 5w^2 - 6w
\]

Thus, the equation that describes the relationship between the width \( w \) and the area \( A \) is:
\[
A = 5w^2 - 6w
\]

So the correct answer is **B. \( A = 5w^2 - 6w \)**.