The altitude (i.e., height) of a triangle is increasing at a rate of 3 cm/minute while the area of the triangle is increasing at a rate of 3 square cm/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 94 square centimeters?

To solve this problem, we'll need to use related rates in calculus. Here's the step-by-step process:

### Step 1: Identify the given information.
- The altitude \( h \) of the triangle is increasing at a rate of \( \frac{dh}{dt} = 3 \) cm/min.
- The area \( A \) of the triangle is increasing at a rate of \( \frac{dA}{dt} = 3 \) square cm/min.
- When \( h = 7 \

Explore how to calculate the rate of change of a triangle's base when altitude and area are given rates. This calculus problem involves related rates and is suitable for advanced high school students.

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