One leg of a right triangle is always $6$ feet long and the other leg is increasing at a rate of $2$ ft/s. Find the rate of change in ft/s of the hypotenuse when it is $10$ feet long.
The answer is $1.6$
So I try the following formula based on the Pythagorean theorem:
$(6^2)^2 + (2t)^2 = 10^2$
Compute for $t$; which is the time elapsed as the hypotenuse got to $10$. I get $t = 4$. So I divide $10/4$ and I get $2.5$. Am I doing something wrong? Any Hint?