The area of a triangle is growing at a rate of 4 cm2/min. If the height of this triangle is always twice the base, find the rate of change of the base when the base is 6cm.
let the base be x cm
then the height is 2x cm
Area = (1/2)(base)(height)
= (1/2)(x)(2x) = x^2
d(Area)/dt = 2x dx/dt
given: d(area)/dt = 4 cm^2 / min
find : dx/dt when x = 6 cm
4 = 2(6) dx/dt
dx/dt = 1/3 cm/min