Question

Find the rate at which the diagonal of a square is changing with respect to its side when the side is 5 cm long.

Answer 1

okay

Answer 2

by pythagorean thm
let D be the diagonal of the sq with lengths x
\[D=\sqrt{(x^2+x^2)}=\sqrt{(2x^2)}=\sqrt2* x\]

Answer 3

this is a linear function

Answer 4

with slope root 2

Answer 5

so the rate of increase of D with respect to side x = root 2

Answer 6

Okay. Thank you!!
Did you evaluate this in relation to the triangle being an isosceles triangle and x and y being congruent and therefore the hypotenuse had to be 5* square root X?
I wasn't sure if I needed to take the dy/dx of the Pythagorean because I thought it was a related rate problem. When I did take the derivative though and evaluated it with respect to x=5, I got 10, but that didn't seem right.
Thank you again!

Answer 7

right :)
dy/dx = root 2
its constant no matter what the x

Answer 8

Great. Thank you!!!
Is that because of the 45-45-90 triangle properties?