Question

The area of a triangle increases at 8cm^2/min and the length of its base increases at 0.6 cm/min. determine the rate of increase of the altitude of the triangle when the area is 72.cm^2and the altitude is 12cm

Answer 1

Area = (1/2)base x height
2A = bh
2A dA/dt = b dh/dt + h db/dt , #1

given: dA = 8 cm^2/min , db/dt = .6 cm/min
find dh/dt when A = 72 and h = 12

when A = 72 and h = 12
72 = (1/2)(b)(12
b = 12

now back into #1
2A dA/dt = b dh/dt + h db/dt

2(72)(8) = 12(dh/dt) + 12(.6) , skipping the units for easier typing

I will let you finish the arithmetic of solving for dh/dt
the units will be cm/min