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 analyze the situation involving the isosceles triangle and apply the concept of derivatives to find the rate at which the area is decreasing.

### Step 1: Understand the Triangle Configuration
We have an isosceles triangle with a fixed base \( b \) and two equal sides \( a \). The two equal sides are decreasing at a rate of \( \frac{da}{dt} = -3 \) cm/s (negative because they are decreasing).

### Step 2: Find the Height of the Triangle
To find the area of the triangle, we need the height. We can drop a perpendicular from the apex of the triangle to the midpoint of the base. This creates two right triangles.

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