The side of a square is increasing at ther rate of `0.2 cm//s`. The rate of increase of perimeter w.r.t. time is :

Options

A. 0.2 cm/s
B. 0.4 cm/s
C. 0.6 cm/s
D. 0.8 cm/s

Explanation

To find the rate of increase of the perimeter of a square with respect to time, we can follow these steps:

### Step 1: Understand the problem
We know that the side length of a square is increasing at a rate of \(0.2 \, \text{cm/s}\). We need to find how fast the perimeter of the square is increasing.

### Step 2: Write the formula for the perimeter of a square
The perimeter \(P\) of a square with side length \(A\) is given by:
\[ P = 4A \]

### Step 3: Differentiate the perimeter with respect to time
To find the rate of change of the perimeter with respect to time, we differentiate \(P\) with respect to \(t\):
\[ \frac{dP}{dt} = \frac{d}{dt}(4A) = 4 \frac{dA}{dt} \]

### Step 4: Substitute the known rate of change of the side length
We know that \(\frac{dA}{dt} = 0.2 \, \text{cm/s}\). Substituting this value into the equation gives:
\[ \frac{dP}{dt} = 4 \times 0.2 \]

### Step 5: Calculate the rate of change of the perimeter
Now, we can calculate:
\[ \frac{dP}{dt} = 4 \times 0.2 = 0.8 \, \text{cm/s} \]

### Conclusion
The rate of increase of the perimeter with respect to time is:
\[ \frac{dP}{dt} = 0.8 \, \text{cm/s} \]