Related Rates: The altitude of a triangle is increasing while the area of the triangle is increasing. At what rate is the base of the triangle changing?

Question

The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the triangle is increasing at a rate of 2 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 9 centimeters and the area is 90 square centimeters?

Answer 1

Let x = length of base at time t and y = length of altitude at time t and A = area at time t.

Given: dy/dt = 1 and dA/dt = 2

Find dx/dt when y = 9 and A = 90

A = xy When y = 9 and A = 90, x = 10.

dA/dt = x(dy/dt) + y(dx/dt)

So, 90 = (10)(1) + (9)(dx/dt). Therefore, dx/dt = 80 / 9 cm/min