A triangle has base b centimeters and height h centimeters, where the height is three times the base. Both b and h are functions of time t, measured in seconds.

Question

If A represents the area of the triangle, which of the following gives the rate of change of A with respect to to?

Answer 1

h=3b

h' = 3b'

A = hb = 3b(b) = 3b^2

A'(t) = 6bb' = 6b(t)(b'(t))

or A'(t) h'b + bh' = 3b'b + b(3b') = 6bb'

or A' = h'(h/3) + (h/3)h' = (2h/3)h' = (2/3)h(t)h'(t)