Calculus Question

Question

The altitude of a triangle is increasing at a rate of 2 centimeters/minute while the area of the triangle is increasing at a rate of 4.5 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 89 square centimeters?

Answer 1

Let A be the triangle Area

Let h be the triangle height

Let b be the triangle base

Given:

dh/dt = 2 cm/min

dA/dt = 4.5 cm²/min

A= bh/2 --> b = 2A/h

Want db/dt when h = 10 cm and A = 89 cm²

b= 2(89)/10 = 89/5

dA/dt = (bdh/dt + hdb/dt)/2

db/dt = (2dA/dt - bdh/dt)/h

= (2(4.5) - (89/5)(2))/10 = (9 -35.6)/10 = -2.66 cm/min