The altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 7 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 22 centimeters and the area is 66 square centimeters?
The change in altitude: da/dt = 3 cm/min
The change in area: dA/dt = 7 cm^2/min
The change in base: db/dt
From the formula of area of triangle:
A = (a x b)/2
66 = (22 x b)/2
b = 6 cm
Differentiate the formula above with respect to time:
dA/dt = (b. da/dt + a. db/dt)/2
7 = ((6x3) + 22db/dt)/2
db/dt = -2/11 cm/min