To find the length of the base of the triangle, you can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, you are given the area (7.5 square feet) and the height (2.5 feet). Plugging in the values, the equation becomes:
\[ 7.5 = \frac{1}{2} \times \text{base} \times 2.5 \]
First, simplify the equation by multiplying both sides by 2 to eliminate the fraction:
\[ 15 = \text{base} \times 2.5 \]
Next, solve for the base by dividing both sides by 2.5:
\[ \text{base} = \frac{15}{2.5} \]
Calculating the right side gives:
\[ \text{base} = 6 \]
Therefore, the length of the base of the sign is 6 feet.