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Verified Answer :

nobillionaireNobley

Let the side length of the square be x, then A = x^2
but diagonal (z) = sqrt(2x^2)
z^2 = 2x^2
x^2 = 1/2 z^2

Thus, A = 1/2 z^2
dA/dz = 1/2 (2z) = z
The rate of change is z.

When z = 4, the rate is 4.

The rate of change of the area of a square with respect to the length z of a diagonal will be 4.

What is the area?

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

The area of a square with side length a is;

A= s²

The diagonal of the square is;

\(\rm z = \sqrt{2x^2} \\\\ z^2 = 2x^2\\\\ x^2 = \frac{1}{2} z^2\)

Substitute the above value;

\(\rm A = \frac{1}{2} z^2\)

The rate of the change of area with respect to the diagonal is;

\(\rm A = \frac{z^2}{2} \\\\ \frac{dA}{dz} = z \\\\ \frac{dA}{dz} = 4\)

Hence the rate when z = 4 will be 4.

To learn more about the area, refer to the link;

https://brainly.com/question/11952845

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