[jyl]

Ok, it is late and no time to check this, but what do you think of this:

We know equilateral triangle's area A = (3^0.5)/4 * S^2 where S is length of one side.
Write side of triangle as a function of time, S = S(t). We don't know what the S(t) formula is, but no matter.
So can write area as function of time, A(t) = (3^0.5)/4 * [S(t)]^2

Now, differentiate dA(t)/dt. Using the chain rule, we know
dA(t)/dt = dA(S)/dS * dS(t)/dt
The power rule gives us dA(S)/dS = (3^0.5)/4 * 2 * S(t) = (3^0.5)/2 * S(t)
Since we don't know what the S(t) formula is, we do not know exactly what the dS(t)/dt formula is, but no matter.
The chain rule gives us dA(t)/dt = (3^0.5)/2 * S(t) * dS(t)/dt

We are looking at the instant when A = 16. So
16 = (3^0.5)/4 * [S(t)]^2
[S(t)]^2 = 16 *4 / (3^0.5) = 64 / (3^0.5)
S(t) = 8 / (3^0.25)

And at this instant, dA(t)/dt = 4. So
4 = (3^0.5)/2 * S(t) * dS(t)/dt
Substitute in S(t) = 8 / (3^0.25)
And get 4 = [ (3^0.5)/2 ] * [8 / (3^0.25)] * dS(t)/dt
4 = 4 *(3^0.25) * dS(t)/dt
dS(t)/dt = 1/(3^0.25)