Answer is: option2

\( \frac{3}{2} \)

Solution:

Let:

1. \( s \) be the side length of the square.
2. \( A \) be the area of the square.

Since the area of a square is given by:

\[ A = s^2 \]

Differentiate both sides with respect to time \( t \):

\[ \frac{dA}{dt} = 2s \frac{ds}{dt} \]

We are given that the area is increasing three times as fast as the side length:

\[ \frac{dA}{dt} = 3 \frac{ds}{dt} \]

Substituting into the equation:

\[ 3 \frac{ds}{dt} = 2s \frac{ds}{dt} \]

Cancel \( \frac{ds}{dt} \) (assuming \( \frac{ds}{dt} \neq 0 \)):

\[ 3 = 2s \]

\[ s = \frac{3}{2} \]

The correct answer is: \( \frac{3}{2} \)