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 are given:
- Area = 7.5 square feet
- Height = 2.5 feet
Let \( b \) be the length of the base. Plugging in the values we have:
\[ 7.5 = \frac{1}{2} \times b \times 2.5 \]
Multiplying both sides by 2 to eliminate the fraction:
\[ 15 = b \times 2.5 \]
Now, solve for \( b \):
\[ b = \frac{15}{2.5} \]
Calculating the right-hand side:
\[ b = 6 \]
So, the length of the base of the sign is \( 6 \) feet.
The answer is 6 feet.