What is the rate of change of the perimeter of the square at the instant the area is 49 m2?

Let x = the length of a side of the square (m).

The area is

A = x²

The perimeter is

P = 4x

The rate of change of P with respect to x is

P' (x) = 4 (independent of x)

When A = 49 m², then x = 7 m.

The rate of P is 4.

Answer: 4