The sides of an equilateral triangle are increasing at the rate of `2` cm/s. Find the rate at which the area increases, when the side is `10 cm`.

Explanation

To solve the problem step by step, we will follow the mathematical reasoning outlined in the video transcript.

### Step 1: Understand the problem
We are given that the sides of an equilateral triangle are increasing at a rate of 2 cm/s. We need to find the rate at which the area of the triangle increases when the side length is 10 cm.

### Step 2: Write the formula for the area of an equilateral triangle
The area \( A \) of an equilateral triangle with side length \( S \) is given by the formula:
\[
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