Let x = length of side of the square. Then area of the square is
A(x) = x^2
You are also told that dx/dt = 6 cm/s
Now, you want to find dA/dt when A = 16, i.e., when x = 4.
Since
dx/dt = 6cm/s
and
dA/dx = 16cm/s
dA/dx dx/dt
= dA/dt
dA/dt A' = 2xx'
A' = 2x6cm/s
So we need to solve for x because we are trying to find dA
so
16 = x^(2)
(16)^(1/2) = 4
thus
A' = 2(4)(6)
A' = 48
