Answer:
80cm^2/s
Step-by-step explanation:
This is a related rates problem where we are considering the rate at which the area of a square changes with respect to time.
So lets consider the area of a square:
A = s^2 (where s represents the length of one side of the square)
Related rates problem deal with functions of time so if we take the area and side length as a function of time and then differentiate implicitly we get:
The problem states that the side of a square is increasing at a rate off 8cm/s so we can conclude that ds/dt = 8cm/s leaving us with:
Now, to solve for s we have to consider the other value given. If the area of the square is initially 25cm^2 we can plug this into our formula for area to solve for the side length.
25 = s^2
s = +/- 5 (since side lengths are only positive we only consider +5)
s = 5
Now we can plug this back in for s:
Therefore, the rate at which the area of the square is increasing is 80cm^2 per second.