Question

g The altitude 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 cm2/min. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 160 cm2

Answer 1

Answer:

  -0.6 cm/min

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = (1/2)bh

Solving for the base, we find ...

  b = 2A/h

Then the rate of change of the base is ...

  b' = 2(A'h -Ah')/h^2

Filling in the given values, we find the rate of change of the base to be ...

  b' = 2((2 cm^2/min)(20 cm) -(160 cm^2)(1 cm/min))/(20 cm)^2

  = 2(40-160)/400 cm/min

  = -0.6 cm/min

The base is decreasing at 0.6 cm/minute.