Question

A right triangle has a fixed base of length 6 meters and a height that is increasing at a rate of 2
meters/second. At what rate is the length of the hypotenuse increasing when the height is 8 meters?

Answer 1

If the hypotenuse has length z, then

h^2+36 = z^2
when h=8, z=10

2h dh/dt = 2z dz/dt
or,
h dh/dt = z dz/dt
So, when h=8,

8*2 = 10 dz/dt
dz/dt = 1.6 m/s

Answer 2

1/5