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?(1 point)
Responses

A=5(w2−6)
cap A is equal to 5 times open paren w squared minus 6 close paren

A=5w−6
cap A is equal to 5 w minus 6

A=5w2−6w
cap A is equal to 5 w squared minus 6 w

A=5w2

Answer 1

To find the equation that describes the relationship between the width `w` of the garden plot and the area `A`, we need to first express both the length and area in terms of `w`.

1. **Express the length in terms of the width**:
The length \( l \) is given as "6 meters less than 5 times the width". This can be expressed mathematically as:
\[
l = 5w - 6
\]

2. **Determine the area**:
The area \( A \) of a rectangle is calculated using the formula:
\[
A = l \times w
\]
Substituting the expression for length \( l \) gives:
\[
A = (5w - 6) \times w
\]

3. **Expand the equation**:
Now, we expand the equation:
\[
A = 5w^2 - 6w
\]

Thus, the equation that describes the relationship between the width `w` of the plot in meters, and the area `A` in square meters is:
\[
A = 5w^2 - 6w
\]

So, the correct response is:
**A = 5w² - 6w**.