Use the table

Question

l A(l)
2 8
4 16
6 24
8 32
Kate is trying to decide how large she wants the total area of her garden to be. The table shows some of the possibilities she is considering for the length of one side (l) and the total area of the garden, A(l) Which of the following equations describes the relationship between side length and area as outlined in this table using function notation
A(l) = 2l
A(w) =l+2
A(l) =4l
A(w) =l +4

Answer 1

To find the correct equation that describes the relationship between the side length \( l \) and the total area \( A(l) \) based on the provided table, we can analyze the values.

The table shows:

\[ \begin{array}{|c|c|} \hline l & A(l) \ \hline 2 & 8 \ 4 & 16 \ 6 & 24 \ 8 & 32 \ \hline \end{array} \]

From the table, we can observe that:

• When \( l = 2 \), \( A(2) = 8 \)
• When \( l = 4 \), \( A(4) = 16 \)
• When \( l = 6 \), \( A(6) = 24 \)
• When \( l = 8 \), \( A(8) = 32 \)

Now, we notice that for each value of \( l \), the area \( A(l) \) is four times the side length \( l \):

1. For \( l = 2 \): \( 4 \times 2 = 8 \)
2. For \( l = 4 \): \( 4 \times 4 = 16 \)
3. For \( l = 6 \): \( 4 \times 6 = 24 \)
4. For \( l = 8 \): \( 4 \times 8 = 32 \)

This indicates that the relationship is given by the equation:

\[ A(l) = 4l \]

Therefore, the correct answer is:

A(l) = 4l