To find the cost of the border around Gabrielle's garden, we can use the formula you provided, which is \( 1.50(2l + 2w) \).
Given:
- Length \( l = 4 \) yards
- Width \( w = 3 \) yards
First, we need to calculate the perimeter of the garden using the formula for perimeter of a rectangle:
\[ P = 2l + 2w \]
Substituting in the values:
\[ P = 2(4) + 2(3) \]
\[ P = 8 + 6 = 14 \text{ yards} \]
Now, we can calculate the cost using the cost per yard:
\[ \text{Cost} = 1.50 \times P = 1.50 \times 14 \]
Calculating the cost:
\[ \text{Cost} = 1.50 \times 14 = 21.00 \]
Thus, the cost for the border around Gabrielle's garden is $21.00.