Question

the altitude of a triangle is increasing at a rate of 1 cm/min while the area in increasing at a rate of 2 cm^2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100cm^2?

Answer 1

S= 1/2b*h
dS = 1/2(h*db+b*dh)
dS/dt= 1/2(h*db/dt+b*dh/dt)
so
2 =1/2(10 db/dt+b*1) as S=100=1/2 b*10 b=20
so
4= 10db/dt+20 so db/dt = -1.6 cm/min (decreasing)