Question

The height of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 square cm/min. At what rate is the base of the triangle changing when the height is 7 centimeters and the area is 91 square centimeters?

Answer 1

A = (1/2) b h

dA/dt = (1/2)(b dh/dt + h db/dt)

given: dA/dt = 2 , dh/dt = 1 , A = 91 , h = 7 ,

we need the base b,
from A = 1/2)bh
91 = (1/2)(7b)
182 = 7b
b = 26

2 = (1/2)(26(1) + 7db/dt)
4 = 23 + 7db/dt
db/dt = -19/7 cm/min

At that moment, the base is decreasing at 19/7 cm/min