To find the length of the base of the triangle, we can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
We know the area is 7.5 square feet and the height is 2.5 feet. Let \( b \) be the length of the base. Plugging the known values into the formula, we get:
\[ 7.5 = \frac{1}{2} \times b \times 2.5 \]
To solve for \( b \), first simplify the equation:
\[ 7.5 = \frac{2.5b}{2} \]
Multiplying both sides by 2 to eliminate the fraction:
\[ 15 = 2.5b \]
Now, divide both sides by 2.5 to isolate \( b \):
\[ b = \frac{15}{2.5} \]
Calculating \( b \):
\[ b = 6 \text{ feet} \]
So, the length of the base of the sign is 6 feet.