The base of a triangle is shrinking at a rate of 1cm/min and the height if the triangle is increasing at a rate of 5cm/min. Find the rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm.

Answer: Rate of change of Area of the triangle = 2.75cm~/min

Step-by-step explanation:

If the present height of the triangle is 22cm and the height increases by 5cm/min. It means the height was 2cm four minutes earlier: 5cm for 1st min + 5cm for 2nd min + 5cm for 3rd min + 5cm for 4th min = 20cm after 4min.

Therefore height equals 22 - 20 = 2cm four minutes earlier.

Using the same four minutes for the base. Since the base shrinks at 1cm/min, for the base to shrink to 10cm it means it was 14cm four minutes earlier.

The Area of a triangle is given by

A = 1/2 * base * height

Therefore Area = 1/2 * 10*22 = 110cm~

Since it took four minutes to get to this area, the rate of change of the area will be 110:4 = 2.75cm~/min