To find the height of the triangular garden using the given area, we can start with the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Given that the area of the garden can be no more than 120 square feet and the base of the triangle is 16 feet, we can set up the following inequality:
\[ \frac{1}{2} \times 16 \times h \leq 120 \]
Now, simplify the inequality:
\[ 8h \leq 120 \]
Next, to isolate \( h \), divide both sides by 8:
\[ h \leq \frac{120}{8} \]
This simplifies to:
\[ h \leq 15 \]
Thus, the height of the triangle can be no more than 15 feet.
In conclusion, the height \( h \) of the triangular garden must satisfy:
\[ h \leq 15 \text{ feet} \]
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