The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?

Explanation

To solve the problem step by step, we will first establish the relationships and then apply the necessary calculus concepts.

### Step 1: Understand the problem
We have an isosceles triangle with a fixed base \( b \) and two equal sides \( a \). The sides \( a \) are decreasing at a rate of \( \frac{da}{dt} = -3 \) cm/s. We need to find how fast the area of the triangle is decreasing when the two equal sides are equal to the base, i.e., when \( a = b \).

### Step 2: Area of the triangle
The area \( A \) of the triangle can be expressed as:
\[
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