Question

Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square increasing when the area of the square is 16cm^(2)
Please show the steps.

Answer 1

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