Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square increasing when the area of the square is 16 cm^2?

Answer 1

Step 1: What is the area of a square?

Area or A = x² (x represents one side)

Step 2: What is given in the problem and what are we trying to find?

The rate a which each side is increasing or dx/dt = 3 cm/s. (GIVEN)

The area of the square is 16 cm² (GIVEN)

This also means each side of the square or x = 4 cm [A=x²]

We are trying to find the rate the area is changing, so dA/dt

Step 3: Take the derivative of the area equation with respect to time

dA/dt= 2x * dx/dt

Now plug in the values given to solve for dA/dt: x= 4cm and dx/dt= 3 cm/s

2 (4) * (3) = 24 cm²/s

Final Answer: 24 cm²/s

Answer 2

A = s²

dA/dt = 2s ds/dt

dA/dt = 2(4)(3) = 24 cm²/s

Answer 3

Suppose the side of the square is p cm

Then dp/dt = 3

If A is the area you want dA/dt when A = 16.

Well A = p²

dA/dt = 2p dp/dt

When A = 16, p = 4

So dA/dt = 2 x 4 x 3 = 24 cm² /s