The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at a rate of 4.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 8 centimeters and the area is 98 square centimeters?

Answer 1

A = (1/2)bh
2A = bh
when A = 98 and h = 8
196 = 8b
b = 24.5

2 dA/dt = b dh/dt + h db/dt
subbing in your given data:
dh/dt = 2, dA/dt = 4.5 , b = 24.5, h = 8
2(4.5) = 24.5(2) + 8 db/dt

solve for db/dt