Let 's' be the length side of a square
A is its area
From pythagorean theorem, we know the diagonal, y, is:
Also, we know the area of a square is:
We can substitute this equation in previous one to get:
We can implicitly differentiate with respect to time (t) to get:
dA/dt is rate of change of Area with time, which is 32.
dy/dt is rate of change of diagonal [what we want to find]
At the instant diagonals are 12, y = 12
Thus, we have: