Question

Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 81 cm2?

Answer 1

related rates right?

Answer 2

area of a square with side \(x\) is \(A=x^2\)
differentiate with respect to time and you get
\[A'=2xx'\]

Answer 3

you are told \(x'=4\) and since \(A=81\) that makes \(x=\sqrt{81}=9\)

Answer 4

plug them in and get \(A'\) by multiplication

Answer 5

not sure if that was clear, but i hope so
final answer is
\[A'=2\times 9\times 4\]

Answer 6

so I get my answer by multiplying 2 9 and 4

Answer 7

oui

Answer 8

thank you!!!

Answer 9

yw