How Does the Area of a Square Change with Its Diagonal?

[CJ256]

Homework Statement

What is the rate of change of an area of a square with respect to the length of its diagonal (r) when the square has a side length of 5 meters?

Homework Equations

The Attempt at a Solution

Area of a square = s^2
and if Area of a square = s^2 then it would = (r^2)/2

Pythagorean Theorem to find the diagonal of the square:

r^2 = s^2 + s^2
r^2= 2s^2
r=sqrt2s^2
r=sqrt2 * s

and then I did this:

(dA)/(dr) and since we need A in terms of r (i hope that's what the question is asking)

then ((d)/(dr))((r^2)/(2)) = (2r)/2 = r

so then the final answer that I got is A = (5^2)/2 = 12.5

 

[SammyS]

Homework Statement

What is the rate of change of an area of a square with respect to the length of its diagonal (r) when the square has a side length of 5 meters?

Homework Equations

The Attempt at a Solution

Area of a square = s^2
and if Area of a square = s^2 then it would = (r^2)/2

Pythagorean Theorem to find the diagonal of the square:

r^2 = s^2 + s^2
r^2= 2s^2
r=sqrt2s^2
r=sqrt2 * s

and then I did this:

(dA)/(dr) and since we need A in terms of r (i hope that's what the question is asking)

then ((d)/(dr))((r^2)/(2)) = (2r)/2 = r

so then the final answer that I got is A = (5^2)/2 = 12.5

They're not asking for A. Besides, when s = 5 meters, A = 25 m².

They're asking for (dA)/(dr) when s = 5 m. i.e. when r = 5/√(2) m.

You essentially answered it earlier.

 

[CJ256]

They're not asking for A. Besides, when s = 5 meters, A = 25 m².

They're asking for (dA)/(dr) when s = 5 m. i.e. when r = 5/√(2) m.

You essentially answered it earlier.

so would that be the answer then? r = 5/√(2) m?

 

[SammyS]

so would that be the answer then? r = 5/√(2) m?

The answer to the question:

"What is the rate of change of an area of a square with respect to the length of its diagonal (r) when the square has a side length of 5 meters?"​

is 5/√(2) m, but that's not r .