The base of a triangle is decreasing at the rate of 1 ft/sec, while the height is increasing at the rate of 2 ft/sec. At what rate is the area of the triangle changing when the base is 10 ft and the height is 70 ft?

Question

a) -25 ft^2/sec
b) -45 ft^2/sec
c) -50 ft^2/sec
d) 45 ft^2/sec

Answer 1

A = 1/2 bh
so,
dA/dt = 1/2 (b dh/dt + h db/dt)
= 1/2 (10 * 2 + 70 * -1)
= -25 ft^2/s