To find the height of the triangular garden given that the area can be no more than 120 square feet and the base is 16 feet, 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 = 120 square feet
- Base = 16 feet
Substituting these values into the area formula:
\[ 120 = \frac{1}{2} \times 16 \times h \]
Now we can solve for the height \( h \):
- Simplify the equation:
\[ 120 = 8h \]
- Now, divide both sides by 8:
\[ h = \frac{120}{8} \]
- Calculate \( h \):
\[ h = 15 \text{ feet} \]
Therefore, the height of the triangle can be no more than 15 feet.