The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is increasing at a rate of 12 square cm/min. at what rate is the base of the triangle changing when the height is 4 centimeters and the area is 12 square centimeters?

Given Information:

- Rate of height = 2 cm/min

- Rate of area = 12 cm^2/min

- Initial height = 4 cm

- Initial area = 12 cm^2

Calculation:

- Find Initial base using initial height and area:

Since A = 1/2 * b * h; Therefore, 12 = 1/2 * b * 4

Solve for b: 12 = 2b; Therefore, b = 6

- Find rate of base:

after 1 minute: height increased 2 cm, area increased 12 cm^2

which is: height = 6, area = 24 < - - (using these, find base)

24 = 1/2 * b * 6; 24 = 3b; b = 8 (after 1 min)

Therefore, since base changed from 6 to 8 the rate is 2 cm/min

Answer: 2 cm/min